:: TOPREAL4 semantic presentation

begin

definition
let P be ( ( ) ( ) Subset of ) ;
let p, q be ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ;
pred P is_S-P_arc_joining p,q means :: TOPREAL4:def 1
 ex f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st
( f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & P : ( ( ) ( ) RLTopStruct ) = L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( ) Element of P : ( ( ) ( ) RLTopStruct ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & q : ( ( Function-like V30(K20(P : ( ( ) ( ) RLTopStruct ) ,P : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,P : ( ( ) ( ) RLTopStruct ) ) ) ( Relation-like K20(P : ( ( ) ( ) RLTopStruct ) ,P : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) -defined P : ( ( ) ( ) RLTopStruct ) -valued Function-like V30(K20(P : ( ( ) ( ) RLTopStruct ) ,P : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,P : ( ( ) ( ) RLTopStruct ) ) ) Element of K19(K20(K20(P : ( ( ) ( ) RLTopStruct ) ,P : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ,P : ( ( ) ( ) RLTopStruct ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) );
end;

definition
let P be ( ( ) ( ) Subset of ) ;
attr P is being_special_polygon means :: TOPREAL4:def 2
 ex p1, p2 being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ex P1, P2 being ( ( ) ( ) Subset of ) st
( p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in P : ( ( ) ( ) RLTopStruct ) & p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in P : ( ( ) ( ) RLTopStruct ) & P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P2 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P1 : ( ( ) ( ) Subset of ) /\ P2 : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = {p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) & P : ( ( ) ( ) RLTopStruct ) = P1 : ( ( ) ( ) Subset of ) \/ P2 : ( ( ) ( ) Subset of ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) );
end;

definition
let T be ( ( ) ( ) TopStruct ) ;
let P be ( ( ) ( ) Subset of ) ;
attr P is being_Region means :: TOPREAL4:def 3
( P : ( ( ) ( ) Element of T : ( ( ) ( ) RLTopStruct ) ) is open & P : ( ( ) ( ) Element of T : ( ( ) ( ) RLTopStruct ) ) is connected );
end;

theorem :: TOPREAL4:1
for P being ( ( ) ( ) Subset of )
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) st P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) holds
P : ( ( ) ( ) Subset of ) is being_S-P_arc ;

theorem :: TOPREAL4:2
for P being ( ( ) ( ) Subset of )
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) st P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) holds
P : ( ( ) ( ) Subset of ) is_an_arc_of p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ;

theorem :: TOPREAL4:3
for P being ( ( ) ( ) Subset of )
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) st P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) holds
( p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in P : ( ( ) ( ) Subset of ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in P : ( ( ) ( ) Subset of ) ) ;

theorem :: TOPREAL4:4
for P being ( ( ) ( ) Subset of )
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) st P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) holds
p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ;

theorem :: TOPREAL4:5
for P being ( ( ) ( ) Subset of ) st P : ( ( ) ( ) Subset of ) is being_special_polygon holds
P : ( ( ) ( ) Subset of ) is being_simple_closed_curve ;

theorem :: TOPREAL4:6
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,|[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(((p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) + (q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) / 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:7
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,|[(((p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) + (q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) / 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:8
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & |[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,|[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:9
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & |[(q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,|[(q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:10
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
ex P being ( ( ) ( ) Subset of ) st
( P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P : ( ( ) ( ) Subset of ) c= Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:11
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ,1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,|[((((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) + (p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) / 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:12
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ,1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,|[((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) + (p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) / 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:13
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for i being ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) in dom f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V140() V141() V142() V143() V144() V145() ) Element of K19(NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) ) & i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) in dom f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V140() V141() V142() V143() V144() V145() ) Element of K19(NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) ) & i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) > 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ,i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ^ <*p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:14
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,|[((((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) + ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) / 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:15
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = <*(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,|[((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) + ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) / 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(3 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:16
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for i being ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) > 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) & i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) in dom f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( V140() V141() V142() V143() V144() V145() ) Element of K19(NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. i : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:17
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for n being ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in LSeg (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ,n : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
ex h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = (L~ (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) | n : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. n : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:18
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
ex h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) ;

theorem :: TOPREAL4:19
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st ( ( p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) or ( p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) = (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & (LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = {(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ^ <*p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) holds
( h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) )) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: TOPREAL4:20
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & |[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ^ <*|[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & ((LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,|[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (|[(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = {(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) holds
( L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) )) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: TOPREAL4:21
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f, h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & |[((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) <> (f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `2 : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) & h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) = f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ^ <*|[((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) *> : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like non empty V33() FinSequence-like FinSubsequence-like ) FinSequence of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) & ((LSeg ((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,|[((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (LSeg (|[((f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) `1) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ,(p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) `2) : ( ( ) ( ext-real V25() real ) Element of REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) ]| : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined Function-like non empty V33() V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like FinSubsequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) )) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) /\ (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) = {(f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) } : ( ( ) ( non empty ) set ) holds
( L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) )) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: TOPREAL4:22
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for f being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st not f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. (len f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ext-real non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) is being_S-Seq & not p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) holds
ex h being ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) st
( L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) is_S-P_arc_joining f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) /. 1 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Element of the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & L~ h : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= (L~ f : ( ( ) ( Relation-like NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) -defined the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) -valued Function-like V33() FinSequence-like FinSubsequence-like ) FinSequence of ( ( ) ( non empty ) set ) ) ) : ( ( ) ( ) Element of K19( the carrier of (TOP-REAL 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict ) ( non empty TopSpace-like V106() V152() V153() V154() V155() V156() V157() V158() strict ) RLTopStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) \/ (Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) )) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ;

theorem :: TOPREAL4:23
for R being ( ( ) ( ) Subset of )
for p, p1, p2 being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for P being ( ( ) ( ) Subset of )
for r being ( ( ) ( ext-real V25() real ) Real)
for u being ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & p2 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) & Ball (u : ( ( ) ( ) Point of ( ( ) ( non empty ) set ) ) ,r : ( ( ) ( ext-real V25() real ) Real) ) : ( ( ) ( ) Element of K19( the carrier of (Euclid 2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( strict Reflexive discerning symmetric triangle ) ( non empty strict Reflexive discerning symmetric triangle ) MetrStruct ) : ( ( ) ( non empty ) set ) ) : ( ( ) ( ) set ) ) c= R : ( ( ) ( ) Subset of ) holds
ex P1 being ( ( ) ( ) Subset of ) st
( P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p1 : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P1 : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ;

theorem :: TOPREAL4:24
for R, P being ( ( ) ( ) Subset of )
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) st R : ( ( ) ( ) Subset of ) is being_Region & P : ( ( ) ( ) Subset of ) = { q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) : ( q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & ( for P1 being ( ( ) ( ) Subset of ) holds
( not P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) or not P1 : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ) ) } holds
P : ( ( ) ( ) Subset of ) is open ;

theorem :: TOPREAL4:25
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for R, P being ( ( ) ( ) Subset of ) st R : ( ( ) ( ) Subset of ) is being_Region & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & P : ( ( ) ( ) Subset of ) = { q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) : ( q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) or ex P1 being ( ( ) ( ) Subset of ) st
( P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P1 : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ) } holds
P : ( ( ) ( ) Subset of ) is open ;

theorem :: TOPREAL4:26
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for R, P being ( ( ) ( ) Subset of ) st p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & P : ( ( ) ( ) Subset of ) = { q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) : ( q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) or ex P1 being ( ( ) ( ) Subset of ) st
( P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P1 : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ) } holds
P : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ;

theorem :: TOPREAL4:27
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for R, P being ( ( ) ( ) Subset of ) st R : ( ( ) ( ) Subset of ) is being_Region & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & P : ( ( ) ( ) Subset of ) = { q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) : ( q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) or ex P1 being ( ( ) ( ) Subset of ) st
( P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P1 : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ) } holds
R : ( ( ) ( ) Subset of ) c= P : ( ( ) ( ) Subset of ) ;

theorem :: TOPREAL4:28
for p being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for R, P being ( ( ) ( ) Subset of ) st R : ( ( ) ( ) Subset of ) is being_Region & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & P : ( ( ) ( ) Subset of ) = { q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) where q is ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) : ( q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) = p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) or ex P1 being ( ( ) ( ) Subset of ) st
( P1 : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P1 : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ) } holds
R : ( ( ) ( ) Subset of ) = P : ( ( ) ( ) Subset of ) ;

theorem :: TOPREAL4:29
for p, q being ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) )
for R being ( ( ) ( ) Subset of ) st R : ( ( ) ( ) Subset of ) is being_Region & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) in R : ( ( ) ( ) Subset of ) & p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) <> q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) holds
ex P being ( ( ) ( ) Subset of ) st
( P : ( ( ) ( ) Subset of ) is_S-P_arc_joining p : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) ,q : ( ( ) ( V40(2 : ( ( ) ( non empty ext-real positive non negative ordinal natural V25() real V92() V93() V140() V141() V142() V143() V144() V145() ) Element of NAT : ( ( ) ( V140() V141() V142() V143() V144() V145() V146() ) Element of K19(REAL : ( ( ) ( V140() V141() V142() V146() ) set ) ) : ( ( ) ( ) set ) ) ) ) FinSequence-like V132() ) Point of ( ( ) ( non empty ) set ) ) & P : ( ( ) ( ) Subset of ) c= R : ( ( ) ( ) Subset of ) ) ;