:: GOBOARD5 semantic presentation

begin

definition
let G be ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ;
let i be ( ( V24() ) ( ext-real non negative V20() V24() V25() V32() ) Nat) ;
func v_strip (G,i) -> ( ( ) ( ) Subset of ) equals :: GOBOARD5:def 1
 { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : ( (G : ( ( ) ( ) RLTopStruct ) * (i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= r : ( ( ) ( ext-real V25() V32() ) Real) & r : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( ) ( ) RLTopStruct ) * ((i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ) } if ( 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) & i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) < len G : ( ( ) ( ) RLTopStruct ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )
{ |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : (G : ( ( ) ( ) RLTopStruct ) * (i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= r : ( ( ) ( ext-real V25() V32() ) Real) } if i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) >= len G : ( ( ) ( ) RLTopStruct ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
otherwise { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : r : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( ) ( ) RLTopStruct ) * ((i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) } ;
func h_strip (G,i) -> ( ( ) ( ) Subset of ) equals :: GOBOARD5:def 2
 { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : ( (G : ( ( ) ( ) RLTopStruct ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= s : ( ( ) ( ext-real V25() V32() ) Real) & s : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( ) ( ) RLTopStruct ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ) } if ( 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) & i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) < width G : ( ( ) ( ) RLTopStruct ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )
{ |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : (G : ( ( ) ( ) RLTopStruct ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= s : ( ( ) ( ext-real V25() V32() ) Real) } if i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) >= width G : ( ( ) ( ) RLTopStruct ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
otherwise { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : s : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( ) ( ) RLTopStruct ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) } ;
end;

theorem :: GOBOARD5:1
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) = (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ;

theorem :: GOBOARD5:2
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) = (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ;

theorem :: GOBOARD5:3
for j, i1, i2 being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_increasing-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) < (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ;

theorem :: GOBOARD5:4
for j1, j2, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_increasing-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) < (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ;

theorem :: GOBOARD5:5
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : ( (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= s : ( ( ) ( ext-real V25() V32() ) Real) & s : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ) } ;

theorem :: GOBOARD5:6
for i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,(width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= s : ( ( ) ( ext-real V25() V32() ) Real) } ;

theorem :: GOBOARD5:7
for i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,0 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : s : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) } ;

theorem :: GOBOARD5:8
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : ( (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= r : ( ( ) ( ext-real V25() V32() ) Real) & r : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) ) } ;

theorem :: GOBOARD5:9
for j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,(len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) <= r : ( ( ) ( ext-real V25() V32() ) Real) } ;

theorem :: GOBOARD5:10
for j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,0 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = { |[r : ( ( ) ( ext-real V25() V32() ) Real) ,s : ( ( ) ( ext-real V25() V32() ) Real) ]| : ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) Function-like non empty V33() 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like FinSubsequence-like V177() V178() V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) where r, s is ( ( ) ( ext-real V25() V32() ) Real) : r : ( ( ) ( ext-real V25() V32() ) Real) <= (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) } ;

definition
let G be ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ;
let i, j be ( ( V24() ) ( ext-real non negative V20() V24() V25() V32() ) Nat) ;
func cell (G,i,j) -> ( ( ) ( ) Subset of ) equals :: GOBOARD5:def 3
(v_strip (G : ( ( ) ( ) RLTopStruct ) ,i : ( ( ) ( ) Element of G : ( ( ) ( ) RLTopStruct ) ) )) : ( ( ) ( ) Subset of ) /\ (h_strip (G : ( ( ) ( ) RLTopStruct ) ,j : ( ( Function-like V29([:G : ( ( ) ( ) RLTopStruct ) ,G : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,G : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:G : ( ( ) ( ) RLTopStruct ) ,G : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(G : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:G : ( ( ) ( ) RLTopStruct ) ,G : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,G : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:G : ( ( ) ( ) RLTopStruct ) ,G : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,G : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) )) : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;
end;

definition
let IT be ( ( ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ;
attr IT is s.c.c. means :: GOBOARD5:def 4
 for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & ( ( i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) > 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len IT : ( ( ) ( ) RLTopStruct ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) or j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len IT : ( ( ) ( ) RLTopStruct ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) holds
LSeg (IT : ( ( ) ( ) RLTopStruct ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) misses LSeg (IT : ( ( ) ( ) RLTopStruct ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;
end;

definition
let IT be ( ( non empty ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ;
attr IT is standard means :: GOBOARD5:def 5
IT : ( ( ) ( ) RLTopStruct ) is_sequence_on GoB IT : ( ( ) ( ) RLTopStruct ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ;
end;

registration
cluster V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non constant non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard for ( ( ) ( ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ;
end;

theorem :: GOBOARD5:11
for f being ( ( non empty ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for n being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st n : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) in dom f : ( ( non empty ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V187() V188() V189() V190() V191() V192() ) Element of bool NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) holds
ex i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st
( [i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( non empty ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. n : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) ;

theorem :: GOBOARD5:12
for f being ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) )
for n being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st n : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) in dom f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V187() V188() V189() V190() V191() V192() ) Element of bool NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) & n : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) in dom f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V187() V188() V189() V190() V191() V192() ) Element of bool NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) holds
for m, k, i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st [m : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) /. n : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (m : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) /. (n : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like standard ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
(abs (m : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) - i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() V32() ) set ) ) : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) + (abs (k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) - j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() V32() ) set ) ) : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) = 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ;

definition
mode special_circular_sequence is ( ( non empty circular special unfolded s.c.c. ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. ) FinSequence of ( ( ) ( non empty ) set ) ) ;
end;

definition
let f be ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ;
let k be ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ;
assume that
1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) and
k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ;
func right_cell (f,k) -> ( ( ) ( ) Subset of ) means :: GOBOARD5:def 6
 for i1, j1, i2, j2 being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st [i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( ) ( ) RLTopStruct ) /. k : ( ( ) ( ) Element of f : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( ) ( ) RLTopStruct ) /. (k : ( ( ) ( ) Element of f : ( ( ) ( ) RLTopStruct ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & not ( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) & not ( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) & not ( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) holds
( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,(i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) );
func left_cell (f,k) -> ( ( ) ( ) Subset of ) means :: GOBOARD5:def 7
 for i1, j1, i2, j2 being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) st [i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( ) ( ) RLTopStruct ) /. k : ( ( ) ( ) Element of f : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( ) ( ) RLTopStruct ) /. (k : ( ( ) ( ) Element of f : ( ( ) ( ) RLTopStruct ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & not ( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,(i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) & not ( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) & not ( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -' 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) holds
( i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = i2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) = j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & it : ( ( Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) ( V1() V4([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ) V5(f : ( ( ) ( ) RLTopStruct ) ) Function-like V29([:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) ) ) Element of bool [:[:f : ( ( ) ( ) RLTopStruct ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) ,f : ( ( ) ( ) RLTopStruct ) :] : ( ( ) ( ) set ) : ( ( ) ( ) set ) ) = cell ((GoB f : ( ( ) ( ) RLTopStruct ) ) : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i1 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j2 : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) );
end;

theorem :: GOBOARD5:13
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_increasing-in-column & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:14
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_increasing-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:15
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_increasing-in-line & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:16
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_increasing-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:17
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_increasing-in-line & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:18
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:19
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:20
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_increasing-in-column & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:21
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:22
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) c= cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ;

theorem :: GOBOARD5:23
for i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_equal-in-line & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is X_increasing-in-column & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) /\ (v_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) = { q : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Point of ( ( ) ( non empty ) set ) ) : q : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) = (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) } ;

theorem :: GOBOARD5:24
for j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) st G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is V3() & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_equal-in-column & G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) is Y_increasing-in-line & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= width G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) /\ (h_strip (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) = { q : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Point of ( ( ) ( non empty ) set ) ) : q : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) = (G : ( ( tabular ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular ) Matrix of ) * (1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() V32() ) Element of REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) ) } ;

theorem :: GOBOARD5:25
for i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) /\ (cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) = LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD5:26
for j, i being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for G being ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) st j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < width G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) < len G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) /\ (cell (G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) = LSeg ((G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(G : ( ( non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) Go-board) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;

theorem :: GOBOARD5:27
for k, i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for f being ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & [(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. (k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( left_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) & right_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) ;

theorem :: GOBOARD5:28
for k, i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for f being ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & [i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. (k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( left_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) & right_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) ;

theorem :: GOBOARD5:29
for k, i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for f being ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & [i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. (k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * (i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( left_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) & right_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) ;

theorem :: GOBOARD5:30
for k, i, j being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for f being ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & [(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & [(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ] : ( ( ) ( ) set ) in Indices (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) : ( ( ) ( ) set ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,(j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) /. (k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = (GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) * ((i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) -element FinSequence-like V179() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( left_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,(i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) & right_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) = cell ((GoB f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ) : ( ( tabular ) ( V1() non empty-yielding V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5(K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) Function-like V33() FinSequence-like FinSubsequence-like tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column ) FinSequence of K227( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( functional non empty FinSequence-membered ) M10( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) )) ) ,i : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ,j : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Subset of ) ) ;

theorem :: GOBOARD5:31
for k being ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) )
for f being ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) st 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) & k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) <= len f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) holds
(left_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) /\ (right_cell (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) = LSeg (f : ( ( non empty circular special unfolded s.c.c. standard ) ( V1() V4( NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) V5( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) Function-like non empty V33() FinSequence-like FinSubsequence-like circular special unfolded s.c.c. standard ) special_circular_sequence) ,k : ( ( ) ( ext-real non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of bool the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative V20() V24() V25() V32() V44() V161() V187() V188() V189() V190() V191() V192() ) Element of NAT : ( ( ) ( V187() V188() V189() V190() V191() V192() V193() ) Element of bool REAL : ( ( ) ( non empty V33() V187() V188() V189() V193() ) set ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty V90() V121() V122() V123() V124() V125() V126() V127() TopSpace-like strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) : ( ( ) ( ) set ) ) ;