:: GOBOARD6 semantic presentation

begin

theorem :: GOBOARD6:1
for M being ( ( non empty Reflexive ) ( non empty Reflexive ) MetrStruct )
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) )
for r being ( ( real ) ( V11() real ext-real ) number ) st r : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of b1 : ( ( non empty Reflexive ) ( non empty Reflexive ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:2
for n being ( ( natural ) ( natural V11() real ext-real ) Nat)
for p being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) )
for q being ( ( ) ( V42(b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for r being ( ( real ) ( V11() real ext-real ) number ) st p : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = q : ( ( ) ( V42(b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) & r : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Ball (p : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is ( ( ) ( ) a_neighborhood of q : ( ( ) ( V42(b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ) ;

theorem :: GOBOARD6:3
for n being ( ( natural ) ( natural V11() real ext-real ) Nat)
for r being ( ( ) ( V11() real ext-real ) Real)
for B being ( ( ) ( ) Subset of )
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st B : ( ( ) ( ) Subset of ) = Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
B : ( ( ) ( ) Subset of ) is open ;

theorem :: GOBOARD6:4
for M being ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) )
for P being ( ( ) ( ) Subset of ) holds
( u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) in Int P : ( ( ) ( ) Subset of ) : ( ( ) ( open ) Element of K6( the carrier of (TopSpaceMetr b1 : ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace) ) : ( ( ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) iff ex r being ( ( real ) ( V11() real ext-real ) number ) st
( r : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of b1 : ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= P : ( ( ) ( ) Subset of ) ) ) ;

theorem :: GOBOARD6:5
for n being ( ( natural ) ( natural V11() real ext-real ) Nat)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) )
for P being ( ( ) ( ) Subset of ) holds
( u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) in Int P : ( ( ) ( ) Subset of ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) iff ex r being ( ( real ) ( V11() real ext-real ) number ) st
( r : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= P : ( ( ) ( ) Subset of ) ) ) ;

theorem :: GOBOARD6:6
for r1, s1, r2, s2 being ( ( ) ( V11() real ext-real ) Real)
for u, v being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = |[r1 : ( ( ) ( V11() real ext-real ) Real) ,s1 : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & v : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = |[r2 : ( ( ) ( V11() real ext-real ) Real) ,s2 : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
dist (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,v : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) = sqrt (((r1 : ( ( ) ( V11() real ext-real ) Real) - r2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ^2) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) + ((s1 : ( ( ) ( V11() real ext-real ) Real) - s2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ^2) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ;

theorem :: GOBOARD6:7
for r, s, r2, r1 being ( ( ) ( V11() real ext-real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= r2 : ( ( ) ( V11() real ext-real ) Real) & r2 : ( ( ) ( V11() real ext-real ) Real) < r1 : ( ( ) ( V11() real ext-real ) Real) holds
|[(r : ( ( ) ( V11() real ext-real ) Real) + r2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:8
for r, s, s2, s1 being ( ( ) ( V11() real ext-real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= s2 : ( ( ) ( V11() real ext-real ) Real) & s2 : ( ( ) ( V11() real ext-real ) Real) < s1 : ( ( ) ( V11() real ext-real ) Real) holds
|[r : ( ( ) ( V11() real ext-real ) Real) ,(s : ( ( ) ( V11() real ext-real ) Real) + s2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,s1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:9
for r, s, r2, r1 being ( ( ) ( V11() real ext-real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= r2 : ( ( ) ( V11() real ext-real ) Real) & r2 : ( ( ) ( V11() real ext-real ) Real) < r1 : ( ( ) ( V11() real ext-real ) Real) holds
|[(r : ( ( ) ( V11() real ext-real ) Real) - r2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:10
for r, s, s2, s1 being ( ( ) ( V11() real ext-real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= s2 : ( ( ) ( V11() real ext-real ) Real) & s2 : ( ( ) ( V11() real ext-real ) Real) < s1 : ( ( ) ( V11() real ext-real ) Real) holds
|[r : ( ( ) ( V11() real ext-real ) Real) ,(s : ( ( ) ( V11() real ext-real ) Real) - s2 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,s1 : ( ( ) ( V11() real ext-real ) Real) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:11
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
(G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ;

theorem :: GOBOARD6:12
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (v_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) } ;

theorem :: GOBOARD6:13
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (v_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) } ;

theorem :: GOBOARD6:14
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (v_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:15
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (h_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) } ;

theorem :: GOBOARD6:16
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (h_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) } ;

theorem :: GOBOARD6:17
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (h_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:18
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:19
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) & (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) ) } ;

theorem :: GOBOARD6:20
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) & (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:21
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:22
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) ) } ;

theorem :: GOBOARD6:23
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:24
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:25
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) & (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) ) } ;

theorem :: GOBOARD6:26
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = { |[r : ( ( ) ( V11() real ext-real ) Real) ,s : ( ( ) ( V11() real ext-real ) Real) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( V11() real ext-real ) Real) : ( (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < r : ( ( ) ( V11() real ext-real ) Real) & r : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) & (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < s : ( ( ) ( V11() real ext-real ) Real) & s : ( ( ) ( V11() real ext-real ) Real) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ) } ;

theorem :: GOBOARD6:27
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) in Int (h_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) > (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ;

theorem :: GOBOARD6:28
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) in Int (h_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ;

theorem :: GOBOARD6:29
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) in Int (v_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) > (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ;

theorem :: GOBOARD6:30
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) in Int (v_strip (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) < (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( V11() real ext-real ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ;

theorem :: GOBOARD6:31
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
(1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:32
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:33
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:34
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:35
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:36
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:37
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:38
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:39
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:40
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:41
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:42
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:43
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:44
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:45
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:46
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:47
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:48
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:49
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:50
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:51
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:52
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:53
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:54
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:55
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:56
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:57
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:58
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:59
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:60
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:61
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:62
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:63
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:64
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:65
for j, i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:66
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:67
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,((width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,((width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:68
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:69
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:70
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:71
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:72
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:73
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:74
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:75
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:76
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,((width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,((width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:77
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,((width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,((width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:78
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:79
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:80
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:81
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= ((Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ {((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) : ( ( ) ( non empty ) set ) ;

theorem :: GOBOARD6:82
for i, j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:83
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:84
for i being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:85
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg ((((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:86
for j being ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) )
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) <= width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
LSeg (p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ,(((1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) / 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non negative ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) * ((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:87
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) - |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:88
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:89
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:90
for p being ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for G being ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) holds LSeg (p : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) ,((G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) + |[1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,(- 1 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() real ext-real non positive ) Element of REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) ]| : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( V42(2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V148() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets Int (cell (G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(len G : ( ( V18() V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V16() V18() V19( NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) V20(K246( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) M11( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) V21() FinSequence-like V144() X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ) : ( ( ) ( natural V11() real ext-real V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ,0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( open ) Element of K6( the carrier of (TOP-REAL 2 : ( ( ) ( non empty natural V11() real ext-real positive non negative V33() V156() V157() V158() V159() V160() V161() V162() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD6:91
for M being ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace)
for p being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) )
for q being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) )
for r being ( ( real ) ( V11() real ext-real ) number ) st p : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) = q : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) & r : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Ball (p : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of b1 : ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is ( ( ) ( ) a_neighborhood of q : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ) ;

theorem :: GOBOARD6:92
for M being ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace)
for A being ( ( ) ( ) Subset of )
for p being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) holds
( p : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) in Cl A : ( ( ) ( ) Subset of ) : ( ( ) ( closed ) Element of K6( the carrier of (TopSpaceMetr b1 : ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace) ) : ( ( ) ( non empty strict TopSpace-like ) TopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) iff for r being ( ( real ) ( V11() real ext-real ) number ) st r : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
Ball (p : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of b1 : ( ( non empty Reflexive discerning V88() triangle ) ( non empty Reflexive discerning V88() triangle Discerning ) MetrSpace) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets A : ( ( ) ( ) Subset of ) ) ;

theorem :: GOBOARD6:93
for n being ( ( natural ) ( natural V11() real ext-real ) Nat)
for A being ( ( ) ( ) Subset of )
for p being ( ( ) ( V42(b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) )
for p9 being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V42(b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) = p9 : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) holds
for s being ( ( real ) ( V11() real ext-real ) number ) st s : ( ( real ) ( V11() real ext-real ) number ) > 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) holds
( p : ( ( ) ( V42(b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) FinSequence-like V148() ) Point of ( ( ) ( non empty ) set ) ) in Cl A : ( ( ) ( ) Subset of ) : ( ( ) ( closed ) Element of K6( the carrier of (TOP-REAL b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) : ( ( strict ) ( non empty TopSpace-like V111() V136() V137() V138() V139() V140() V141() V142() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) iff for r being ( ( real ) ( V11() real ext-real ) number ) st 0 : ( ( ) ( empty natural V11() real ext-real non positive non negative V33() V156() V157() V158() V159() V160() V161() V162() V163() ) Element of NAT : ( ( ) ( V157() V158() V159() V160() V161() V162() V163() ) Element of K6(REAL : ( ( ) ( V157() V158() V159() V163() ) set ) ) : ( ( ) ( ) set ) ) ) < r : ( ( real ) ( V11() real ext-real ) number ) & r : ( ( real ) ( V11() real ext-real ) number ) < s : ( ( real ) ( V11() real ext-real ) number ) holds
Ball (p9 : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( real ) ( V11() real ext-real ) number ) ) : ( ( ) ( ) Element of K6( the carrier of (Euclid b1 : ( ( natural ) ( natural V11() real ext-real ) Nat) ) : ( ( strict Reflexive discerning V88() triangle ) ( non empty strict Reflexive discerning V88() triangle Discerning ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) meets A : ( ( ) ( ) Subset of ) ) ;