CLVECT

func Cseq * seq -> ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of X : ( ( ) ( ) CUNITSTR ) : ( ( ) ( ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of X : ( ( ) ( ) CUNITSTR ) : ( ( ) ( ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of X : ( ( ) ( ) CUNITSTR ) : ( ( ) ( ) set ) ) ) sequence of ( ( ) ( ) set ) ) means :: CLVECT_3:def 8
for n being ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) holds it : ( ( V18() V27(K7(COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) ) ( V13() V16(K7(COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ) V17(X : ( ( ) ( ) CUNITSTR ) ) V18() V27(K7(COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) ) Element of K6(K7(K7(COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the U1 of X : ( ( ) ( ) CUNITSTR ) : ( ( ) ( ) set ) ) = (Cseq : ( ( V18() V27(K7(X : ( ( ) ( ) CUNITSTR ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) ) ( V13() V16(K7(X : ( ( ) ( ) CUNITSTR ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ) V17(X : ( ( ) ( ) CUNITSTR ) ) V18() V27(K7(X : ( ( ) ( ) CUNITSTR ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) ) Element of K6(K7(K7(X : ( ( ) ( ) CUNITSTR ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ,X : ( ( ) ( ) CUNITSTR ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V11() ) Element of COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) * (seq : ( ( ) ( ) Element of X : ( ( ) ( ) CUNITSTR ) ) . n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the U1 of X : ( ( ) ( ) CUNITSTR ) : ( ( ) ( ) set ) ) : ( ( ) ( ) Element of the U1 of X : ( ( ) ( ) CUNITSTR ) : ( ( ) ( ) set ) ) ;

end;

theorem :: CLVECT_3:43

theorem :: CLVECT_3:44

theorem :: CLVECT_3:45

theorem :: CLVECT_3:46

theorem :: CLVECT_3:47

theorem :: CLVECT_3:48

theorem :: CLVECT_3:49

theorem :: CLVECT_3:50

theorem :: CLVECT_3:51

for Cseq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence)
for X being ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace)
for seq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) st seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) is Cauchy & Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) is Cauchy holds
Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₂ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like V160() ) ComplexHilbertSpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) is Cauchy ;

theorem :: CLVECT_3:52

for X being ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace)
for seq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) )
for Cseq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence)
for n being ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) holds (Partial_Sums ((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) - (Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ^\ 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) subsequence of b₃ : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ) ) : ( ( V18() ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ,COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) : ( ( ) ( complex-valued ) set ) ) : ( ( ) ( ) set ) ) * (Partial_Sums seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) = ((Partial_Sums (Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) - ((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * (Partial_Sums seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) . (n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ;

theorem :: CLVECT_3:53

for X being ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace)
for seq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) )
for Cseq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence)
for n being ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) holds (Partial_Sums (Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . (n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) = ((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * (Partial_Sums seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) . (n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) - ((Partial_Sums (((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ^\ 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) subsequence of b₃ : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ) - Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ) : ( ( V18() ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ,COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) : ( ( ) ( complex-valued ) set ) ) : ( ( ) ( ) set ) ) * (Partial_Sums seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) . n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ;

theorem :: CLVECT_3:54

for X being ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace)
for seq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) )
for Cseq being ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence)
for n being ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) holds Sum ((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ,(n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Point of ( ( ) ( V1() ) set ) ) = ((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) * (Partial_Sums seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) . (n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) + 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) - (Sum ((((Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ^\ 1 : ( ( ) ( V1() V4() V5() V6() V10() V11() V12() ext-real positive non negative integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) ) : ( ( ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) subsequence of b₃ : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ) - Cseq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Complex_Sequence) ) : ( ( V18() ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) complex-valued ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ,COMPLEX : ( ( ) ( V1() V47() V59() V65() ) set ) ) : ( ( ) ( complex-valued ) set ) ) : ( ( ) ( ) set ) ) * (Partial_Sums seq : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) Element of K6(K7(NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) : ( ( ) ( ) set ) ) : ( ( ) ( ) set ) ) ) : ( ( V18() V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) ( V1() V13() V16( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V17( the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) V18() V23( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) V27( NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) , the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ) sequence of ( ( ) ( V1() ) set ) ) ,n : ( ( ) ( V4() V5() V6() V10() V11() V12() ext-real integer V58() V59() V60() V61() V62() V63() V64() ) Element of NAT : ( ( ) ( V1() V4() V5() V6() V59() V60() V61() V62() V63() V64() V65() ) Element of K6(REAL : ( ( ) ( V1() V47() V59() V60() V61() V65() ) set ) ) : ( ( ) ( ) set ) ) ) )) : ( ( ) ( ) Point of ( ( ) ( V1() ) set ) ) : ( ( ) ( ) Element of the U1 of b₁ : ( ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ( V75() V101() V126() V127() V128() V147() V148() V149() V150() ComplexUnitarySpace-like ) ComplexUnitarySpace) : ( ( ) ( V1() ) set ) ) ;