:: PDIFF_1 semantic presentation

REAL is non empty V33() V165() V166() V167() V171() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V165() V166() V167() V168() V169() V170() V171() Element of K6(REAL)
K6(REAL) is set
COMPLEX is non empty V33() V165() V171() set
omega is non empty epsilon-transitive epsilon-connected ordinal V165() V166() V167() V168() V169() V170() V171() set
K6(omega) is set
K6(NAT) is set
K7(NAT,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(NAT,REAL)) is set
K190() is non empty set
K7(K190(),K190()) is set
K7(K7(K190(),K190()),K190()) is set
K6(K7(K7(K190(),K190()),K190())) is set
K7(REAL,K190()) is set
K7(K7(REAL,K190()),K190()) is set
K6(K7(K7(REAL,K190()),K190())) is set
K196() is RLSStruct
the carrier of K196() is set
K6( the carrier of K196()) is set
K200() is Element of K6( the carrier of K196())
K7(K200(),K200()) is set
K7(K7(K200(),K200()),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(K200(),K200()),REAL)) is set
K203() is Element of K6( the carrier of K196())
K7(K203(),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K203(),REAL)) is set
K7(REAL,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(REAL,REAL)) is set
RAT is non empty V33() V165() V166() V167() V168() V171() set
INT is non empty V33() V165() V166() V167() V168() V169() V171() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
K7(1,1) is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K6(K7(1,1)) is set
K7(K7(1,1),1) is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(1,1),REAL)) is set
K7(K7(REAL,REAL),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(REAL,REAL),REAL)) is set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
K7(2,2) is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K7(K7(2,2),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(2,2),REAL)) is set
K456(2) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital TopSpace-like V207() L20()
the carrier of K456(2) is non empty set
ExtREAL is non empty V166() set
K7(COMPLEX,COMPLEX) is complex-valued set
K6(K7(COMPLEX,COMPLEX)) is set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is complex-valued set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(RAT,RAT) is RAT -valued complex-valued ext-real-valued real-valued set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is RAT -valued complex-valued ext-real-valued real-valued set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K7(K7(NAT,NAT),NAT) is RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K6(K7(K7(NAT,NAT),NAT)) is set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative Function-like functional V165() V166() V167() V168() V169() V170() V171() set
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative Function-like functional V139() V164() V165() V166() V167() V168() V169() V170() V171() Element of NAT
- 1 is V11() real ext-real non positive Element of REAL
Seg 1 is V165() V166() V167() V168() V169() V170() Element of K6(NAT)
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative set
REAL I is non empty FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL I),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL I),REAL)) is set
W is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative set
n is non empty Relation-like REAL I -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL I),REAL))
i is non empty Relation-like REAL I -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL I),REAL))
r is Relation-like NAT -defined REAL -valued Function-like V40(I) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL I
n . r is V11() real ext-real Element of REAL
r . W is V11() real ext-real Element of REAL
i . r is V11() real ext-real Element of REAL
(1,1) is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
REAL 1 is non empty FinSequence-membered FinSequenceSet of REAL
1 -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL 1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL 1),REAL)) is set
(1,1) " is Relation-like Function-like set
dom (1,1) is Element of K6((REAL 1))
K6((REAL 1)) is set
rng (1,1) is V165() V166() V167() Element of K6(REAL)
n is set
i is set
(1,1) . n is V11() real ext-real Element of REAL
(1,1) . i is V11() real ext-real Element of REAL
y is V11() real ext-real Element of REAL
<*y*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*y*> . 1 is V11() real ext-real Element of REAL
r is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
(1,1) . r is V11() real ext-real Element of REAL
g is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
g . 1 is V11() real ext-real Element of REAL
Pd is V11() real ext-real Element of REAL
<*Pd*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is V11() real ext-real Element of REAL
<*n*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1,1) . <*n*> is V11() real ext-real Element of REAL
<*n*> . 1 is V11() real ext-real Element of REAL
((1,1) ") . n is set
n is set
i is V11() real ext-real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
(1,1) . r is V11() real ext-real Element of REAL
r . 1 is V11() real ext-real Element of REAL
n is V11() real ext-real Element of REAL
<*n*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1,1) . <*n*> is V11() real ext-real Element of REAL
i is V11() real ext-real Element of REAL
((1,1) ") . i is set
<*i*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Seg n is V165() V166() V167() V168() V169() V170() Element of K6(NAT)
(I,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
r is set
g is V11() real ext-real Element of REAL
n |-> g is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued Element of n -tuples_on REAL
y is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(I,n) . y is V11() real ext-real Element of REAL
y . I is V11() real ext-real Element of REAL
rng (I,n) is V165() V166() V167() Element of K6(REAL)
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Seg n is V165() V166() V167() V168() V169() V170() Element of K6(NAT)
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
(I,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
dom (I,n) is Element of K6((REAL n))
K6((REAL n)) is set
rng (I,n) is V165() V166() V167() Element of K6(REAL)
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Seg n is V165() V166() V167() V168() V169() V170() Element of K6(NAT)
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
(I,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
dom (I,n) is Element of K6((REAL n))
K6((REAL n)) is set
rng (I,n) is V165() V166() V167() Element of K6(REAL)
i is V11() real ext-real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(1,1) . <*i*> is V11() real ext-real Element of REAL
r is V11() real ext-real Element of REAL
((1,1) ") . r is set
<*r*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K7(REAL,(REAL 1)) is set
K6(K7(REAL,(REAL 1))) is set
dom ((1,1) ") is set
rng ((1,1) ") is set
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
I (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) (I (#) ((1,1) ")) is Relation-like Function-like set
K7((REAL 1),(REAL 1)) is set
K6(K7((REAL 1),(REAL 1))) is set
n is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
n * I is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
(n * I) * (1,1) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative set
REAL I is non empty FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL I),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL I),REAL)) is set
n is Relation-like REAL I -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL I),REAL))
n (#) ((1,1) ") is Relation-like Function-like set
K7((REAL I),(REAL 1)) is set
K6(K7((REAL I),(REAL 1))) is set
i is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
i * n is Relation-like REAL I -defined REAL 1 -valued Function-like Element of K6(K7((REAL I),(REAL 1)))
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative set
REAL-NS n is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty set
REAL-NS 1 is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS 1) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative set
(I,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is Element of the carrier of (REAL-NS n)
(I,n) . i is V11() real ext-real Element of REAL
<*((I,n) . i)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len H₁(i) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
i is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
r is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
g is Element of the carrier of (REAL-NS n)
i . g is Element of the carrier of (REAL-NS 1)
(I,n) . g is V11() real ext-real Element of REAL
<*((I,n) . g)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r . g is Element of the carrier of (REAL-NS 1)
n is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
i is Relation-like Function-like set
dom i is set
r is V11() real ext-real Element of REAL
i . r is set
Replace (n,I,r) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
i is Relation-like Function-like set
dom i is set
r is Relation-like Function-like set
dom r is set
g is set
y is V11() real ext-real Element of REAL
i . y is set
Replace (n,I,y) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
i . g is set
r . g is set
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL I is non empty FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
i is Relation-like NAT -defined REAL -valued Function-like V40(I) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL I
(n,i) is Relation-like Function-like set
K7(REAL,(REAL I)) is set
K6(K7(REAL,(REAL I))) is set
r is set
g is V11() real ext-real Element of REAL
(n,i) . g is set
Replace (i,n,g) is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
y is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
len y is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
len i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Pd is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued Element of I -tuples_on REAL
(n,i) . r is set
dom (n,i) is set
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS I is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS I) is non empty set
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS I)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS I))) is set
REAL I is non empty FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is Element of the carrier of (REAL-NS I)
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Element of the carrier of (REAL-NS 1)
y is V11() real ext-real Element of REAL
<*y*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r is Relation-like NAT -defined REAL -valued Function-like V40(I) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL I
(I,n,r) is non empty Relation-like REAL -defined REAL I -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL I)))
K7(REAL,(REAL I)) is set
K6(K7(REAL,(REAL I))) is set
(I,n,r) . y is V40(I) Element of REAL I
r is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS I) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS I)))
g is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS I) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS I)))
y is Element of the carrier of (REAL-NS 1)
r . y is Element of the carrier of (REAL-NS I)
Pd is V11() real ext-real Element of REAL
<*Pd*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
x is Relation-like NAT -defined REAL -valued Function-like V40(I) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL I
(I,n,x) is non empty Relation-like REAL -defined REAL I -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL I)))
K7(REAL,(REAL I)) is set
K6(K7(REAL,(REAL I))) is set
(I,n,x) . Pd is V40(I) Element of REAL I
g . y is Element of the carrier of (REAL-NS I)
<*Pd*> . 1 is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
<*f*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
One is Relation-like NAT -defined REAL -valued Function-like V40(I) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL I
(I,n,One) is non empty Relation-like REAL -defined REAL I -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL I)))
(I,n,One) . f is V40(I) Element of REAL I
I is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL I is non empty FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL I),(REAL n)) is set
K6(K7((REAL I),(REAL n))) is set
I is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL I is non empty FinSequence-membered FinSequenceSet of REAL
I -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL I),(REAL n)) is set
K6(K7((REAL I),(REAL n))) is set
i is Relation-like REAL I -defined REAL n -valued Function-like Element of K6(K7((REAL I),(REAL n)))
r is Relation-like NAT -defined REAL -valued Function-like V40(I) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL I
REAL-NS I is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS I) is non empty V2() set
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS I), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS I), the carrier of (REAL-NS n))) is set
g is Relation-like the carrier of (REAL-NS I) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))
y is Element of the carrier of (REAL-NS I)
diff (g,y) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS I),(REAL-NS n)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS I),(REAL-NS n)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS I),(REAL-NS n)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS I),(REAL-NS n)))
K313( the carrier of (REAL-NS I),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS I), the carrier of (REAL-NS n)
FuncZero ( the carrier of (REAL-NS I),(REAL-NS n)) is Relation-like the carrier of (REAL-NS I) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))
0. (REAL-NS n) is V52( REAL-NS n) Element of the carrier of (REAL-NS n)
K228( the carrier of (REAL-NS n), the carrier of (REAL-NS I),(0. (REAL-NS n))) is non empty Relation-like the carrier of (REAL-NS I) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))
FuncAdd ( the carrier of (REAL-NS I),(REAL-NS n)) is Relation-like K7((Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))))
K7((Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))))) is set
FuncExtMult ( the carrier of (REAL-NS I),(REAL-NS n)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS I), the carrier of (REAL-NS n))),(FuncZero ( the carrier of (REAL-NS I),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS I),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS I),(REAL-NS n))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS I),(REAL-NS n)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS I),(REAL-NS n))) is set
K199(K313( the carrier of (REAL-NS I),(REAL-NS n)),(LinearOperators ((REAL-NS I),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS I),(REAL-NS n))
K197(K313( the carrier of (REAL-NS I),(REAL-NS n)),(LinearOperators ((REAL-NS I),(REAL-NS n)))) is Relation-like K7((LinearOperators ((REAL-NS I),(REAL-NS n))),(LinearOperators ((REAL-NS I),(REAL-NS n)))) -defined LinearOperators ((REAL-NS I),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS I),(REAL-NS n))),(LinearOperators ((REAL-NS I),(REAL-NS n)))),(LinearOperators ((REAL-NS I),(REAL-NS n)))))
K7((LinearOperators ((REAL-NS I),(REAL-NS n))),(LinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K7(K7((LinearOperators ((REAL-NS I),(REAL-NS n))),(LinearOperators ((REAL-NS I),(REAL-NS n)))),(LinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K6(K7(K7((LinearOperators ((REAL-NS I),(REAL-NS n))),(LinearOperators ((REAL-NS I),(REAL-NS n)))),(LinearOperators ((REAL-NS I),(REAL-NS n))))) is set
K198(K313( the carrier of (REAL-NS I),(REAL-NS n)),(LinearOperators ((REAL-NS I),(REAL-NS n)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS I),(REAL-NS n)))) -defined LinearOperators ((REAL-NS I),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS I),(REAL-NS n)))),(LinearOperators ((REAL-NS I),(REAL-NS n)))))
K7(REAL,(LinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS I),(REAL-NS n)))),(LinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS I),(REAL-NS n)))),(LinearOperators ((REAL-NS I),(REAL-NS n))))) is set
RLSStruct(# (LinearOperators ((REAL-NS I),(REAL-NS n))),K199(K313( the carrier of (REAL-NS I),(REAL-NS n)),(LinearOperators ((REAL-NS I),(REAL-NS n)))),K197(K313( the carrier of (REAL-NS I),(REAL-NS n)),(LinearOperators ((REAL-NS I),(REAL-NS n)))),K198(K313( the carrier of (REAL-NS I),(REAL-NS n)),(LinearOperators ((REAL-NS I),(REAL-NS n)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS I),(REAL-NS n))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS I),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))))
K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS I),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n))))) is set
BoundedLinearOperatorsNorm ((REAL-NS I),(REAL-NS n)) is non empty Relation-like BoundedLinearOperators ((REAL-NS I),(REAL-NS n)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),REAL))
K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS I),(REAL-NS n))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS I),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS I),(REAL-NS n))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS I),(REAL-NS n))) is non empty set
f is Relation-like the carrier of (REAL-NS I) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))
One is Element of the carrier of (REAL-NS I)
Pd is non empty Relation-like REAL I -defined REAL n -valued Function-like total quasi_total Element of K6(K7((REAL I),(REAL n)))
diff (f,One) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))
x is Relation-like the carrier of (REAL-NS I) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS I), the carrier of (REAL-NS n)))
I is Element of the carrier of (REAL-NS I)
x is non empty Relation-like REAL I -defined REAL n -valued Function-like total quasi_total Element of K6(K7((REAL I),(REAL n)))
diff (x,I) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS I),(REAL-NS n)))
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
n is Element of the carrier of (REAL-NS 1)
i is V11() real ext-real Element of REAL
I . i is V40(1) Element of REAL 1
r is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*i*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued Element of 1 -tuples_on REAL
Sum (sqr r) is V11() real ext-real Element of REAL
sqrt (Sum (sqr r)) is V11() real ext-real Element of REAL
i ^2 is V11() real ext-real Element of REAL
<*(i ^2)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum <*(i ^2)*> is V11() real ext-real Element of REAL
sqrt (Sum <*(i ^2)*>) is V11() real ext-real Element of REAL
sqrt (i ^2) is V11() real ext-real Element of REAL
||.n.|| is V11() real ext-real Element of REAL
|.r.| is V11() real ext-real non negative Element of REAL
sqr r is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Sum (sqr r) is V11() real ext-real Element of REAL
sqrt (Sum (sqr r)) is V11() real ext-real Element of REAL
abs i is V11() real ext-real Element of REAL
n is Element of the carrier of (REAL-NS 1)
i is Element of the carrier of (REAL-NS 1)
r is V11() real ext-real Element of REAL
I . r is V40(1) Element of REAL 1
g is V11() real ext-real Element of REAL
I . g is V40(1) Element of REAL 1
<*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*r*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
y is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n - i is Element of the carrier of (REAL-NS 1)
<*r*> - <*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r - g is V11() real ext-real Element of REAL
<*(r - g)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
I . (r - g) is V40(1) Element of REAL 1
n is Element of the carrier of (REAL-NS 1)
i is Element of the carrier of (REAL-NS 1)
r is V11() real ext-real Element of REAL
I . r is V40(1) Element of REAL 1
g is V11() real ext-real Element of REAL
I . g is V40(1) Element of REAL 1
<*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*r*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
y is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n + i is Element of the carrier of (REAL-NS 1)
<*r*> + <*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r + g is V11() real ext-real Element of REAL
<*(r + g)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
I . (r + g) is V40(1) Element of REAL 1
n is Element of the carrier of (REAL-NS 1)
i is V11() real ext-real Element of REAL
I . i is V40(1) Element of REAL 1
g is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*i*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
r is V11() real ext-real Element of REAL
r * n is Element of the carrier of (REAL-NS 1)
r * g is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
r * i is V11() real ext-real Element of REAL
<*(r * i)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
I . (r * i) is V40(1) Element of REAL 1
n is Element of the carrier of (REAL-NS 1)
i is V11() real ext-real Element of REAL
I . i is V40(1) Element of REAL 1
(- 1) * n is Element of the carrier of (REAL-NS 1)
(- 1) * i is V11() real ext-real Element of REAL
I . ((- 1) * i) is V40(1) Element of REAL 1
- n is Element of the carrier of (REAL-NS 1)
- i is V11() real ext-real Element of REAL
I . (- i) is V40(1) Element of REAL 1
n is Element of the carrier of (REAL-NS 1)
i is V11() real ext-real Element of REAL
I . i is V40(1) Element of REAL 1
r is V11() real ext-real Element of REAL
r * n is Element of the carrier of (REAL-NS 1)
r * i is V11() real ext-real Element of REAL
I . (r * i) is V40(1) Element of REAL 1
g is Element of the carrier of (REAL-NS 1)
y is V11() real ext-real Element of REAL
I . y is V40(1) Element of REAL 1
- g is Element of the carrier of (REAL-NS 1)
- y is V11() real ext-real Element of REAL
I . (- y) is V40(1) Element of REAL 1
Pd is Element of the carrier of (REAL-NS 1)
f is V11() real ext-real Element of REAL
I . f is V40(1) Element of REAL 1
x is Element of the carrier of (REAL-NS 1)
One is V11() real ext-real Element of REAL
I . One is V40(1) Element of REAL 1
Pd - x is Element of the carrier of (REAL-NS 1)
f - One is V11() real ext-real Element of REAL
I . (f - One) is V40(1) Element of REAL 1
n is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
n is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
i is Element of the carrier of (REAL-NS 1)
n . i is V11() real ext-real Element of REAL
r is V11() real ext-real Element of REAL
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
g is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . g is V11() real ext-real Element of REAL
I . (n . g) is V40(1) Element of REAL 1
I . r is V40(1) Element of REAL 1
||.i.|| is V11() real ext-real Element of REAL
abs r is V11() real ext-real Element of REAL
i is Element of the carrier of (REAL-NS 1)
r is Element of the carrier of (REAL-NS 1)
n . i is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
n . r is V11() real ext-real Element of REAL
y is V11() real ext-real Element of REAL
x is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . x is V11() real ext-real Element of REAL
I . (n . x) is V40(1) Element of REAL 1
I . y is V40(1) Element of REAL 1
Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . Pd is V11() real ext-real Element of REAL
I . (n . Pd) is V40(1) Element of REAL 1
I . g is V40(1) Element of REAL 1
i + r is Element of the carrier of (REAL-NS 1)
n . (i + r) is V11() real ext-real Element of REAL
g + y is V11() real ext-real Element of REAL
I . (g + y) is V40(1) Element of REAL 1
n . (I . (g + y)) is V11() real ext-real Element of REAL
i is Element of the carrier of (REAL-NS 1)
n . i is V11() real ext-real Element of REAL
r is V11() real ext-real Element of REAL
y is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . y is V11() real ext-real Element of REAL
I . (n . y) is V40(1) Element of REAL 1
I . r is V40(1) Element of REAL 1
g is V11() real ext-real Element of REAL
g * i is Element of the carrier of (REAL-NS 1)
n . (g * i) is V11() real ext-real Element of REAL
g * r is V11() real ext-real Element of REAL
I . (g * r) is V40(1) Element of REAL 1
n . (I . (g * r)) is V11() real ext-real Element of REAL
i is Element of the carrier of (REAL-NS 1)
n . i is V11() real ext-real Element of REAL
r is V11() real ext-real Element of REAL
I . r is V40(1) Element of REAL 1
g is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . g is V11() real ext-real Element of REAL
I . (n . g) is V40(1) Element of REAL 1
- i is Element of the carrier of (REAL-NS 1)
n . (- i) is V11() real ext-real Element of REAL
- r is V11() real ext-real Element of REAL
I . (- r) is V40(1) Element of REAL 1
n . (I . (- r)) is V11() real ext-real Element of REAL
i is Element of the carrier of (REAL-NS 1)
n . i is V11() real ext-real Element of REAL
r is Element of the carrier of (REAL-NS 1)
n . r is V11() real ext-real Element of REAL
i - r is Element of the carrier of (REAL-NS 1)
n . (i - r) is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
y is V11() real ext-real Element of REAL
g - y is V11() real ext-real Element of REAL
x is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . x is V11() real ext-real Element of REAL
I . (n . x) is V40(1) Element of REAL 1
I . y is V40(1) Element of REAL 1
Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
n . Pd is V11() real ext-real Element of REAL
I . (n . Pd) is V40(1) Element of REAL 1
I . g is V40(1) Element of REAL 1
I . (g - y) is V40(1) Element of REAL 1
n . (I . (g - y)) is V11() real ext-real Element of REAL
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) is set
n is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
i is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
r is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like RestFunc-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i * r is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of (REAL-NS 1),REAL))
K7( the carrier of (REAL-NS 1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of (REAL-NS 1),REAL)) is set
(i * r) * n is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
g is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
i * g is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(i * g) * n is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
y is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom y is V165() V166() V167() Element of K6(REAL)
Pd is V11() real ext-real Element of REAL
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
x is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
abs f is V11() real ext-real Element of REAL
(abs f) " is V11() real ext-real Element of REAL
y . f is V11() real ext-real Element of REAL
abs (y . f) is V11() real ext-real Element of REAL
((abs f) ") * (abs (y . f)) is V11() real ext-real Element of REAL
n . f is V40(1) Element of REAL 1
x is ext-real Element of ExtREAL
|.x.| is ext-real Element of ExtREAL
One is Element of the carrier of (REAL-NS 1)
||.One.|| is V11() real ext-real Element of REAL
n * i is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
id (dom (1,1)) is Relation-like dom (1,1) -defined dom (1,1) -valued Function-like one-to-one total quasi_total Element of K6(K7((dom (1,1)),(dom (1,1))))
K7((dom (1,1)),(dom (1,1))) is set
K6(K7((dom (1,1)),(dom (1,1)))) is set
id (REAL 1) is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like one-to-one total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
dom (i * g) is Element of K6((REAL 1))
dom r is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
r /. One is Element of the carrier of (REAL-NS 1)
r . One is set
id the carrier of (REAL-NS 1) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like one-to-one total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(id the carrier of (REAL-NS 1)) * r is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
((id the carrier of (REAL-NS 1)) * r) . (n . f) is set
(n * i) * r is Relation-like the carrier of (REAL-NS 1) -defined REAL 1 -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1),(REAL 1)))
K7( the carrier of (REAL-NS 1),(REAL 1)) is set
K6(K7( the carrier of (REAL-NS 1),(REAL 1))) is set
((n * i) * r) . (n . f) is set
r . (n . f) is set
(n * i) . (r . (n . f)) is set
dom i is Element of K6((REAL 1))
g . One is set
i . (g . One) is V11() real ext-real Element of REAL
n . (i . (g . One)) is V40(1) Element of REAL 1
(i * g) . (n . f) is V11() real ext-real Element of REAL
n . ((i * g) . (n . f)) is V40(1) Element of REAL 1
n . (y . f) is V40(1) Element of REAL 1
||.(r /. One).|| is V11() real ext-real Element of REAL
||.One.|| " is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
abs f is V11() real ext-real Element of REAL
(abs f) " is V11() real ext-real Element of REAL
y . f is V11() real ext-real Element of REAL
abs (y . f) is V11() real ext-real Element of REAL
((abs f) ") * (abs (y . f)) is V11() real ext-real Element of REAL
Pd is non empty Relation-like non-empty NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
Pd " is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
y /* Pd is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(Pd ") (#) (y /* Pd) is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((Pd ") (#) (y /* Pd)) is V11() real ext-real Element of REAL
x is V11() real ext-real set
lim Pd is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative Function-like functional V165() V166() V167() V168() V169() V170() V171() Element of REAL
f is V11() real ext-real Element of REAL
One is V11() real ext-real Element of REAL
x is V11() real ext-real set
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Pd . R is V11() real ext-real Element of REAL
rng Pd is V165() V166() V167() Element of K6(REAL)
abs (Pd . R) is V11() real ext-real Element of REAL
(abs (Pd . R)) " is V11() real ext-real Element of REAL
y . (Pd . R) is V11() real ext-real Element of REAL
abs (y . (Pd . R)) is V11() real ext-real Element of REAL
((abs (Pd . R)) ") * (abs (y . (Pd . R))) is V11() real ext-real Element of REAL
(y /* Pd) . R is V11() real ext-real Element of REAL
abs ((y /* Pd) . R) is V11() real ext-real Element of REAL
((abs (Pd . R)) ") * (abs ((y /* Pd) . R)) is V11() real ext-real Element of REAL
abs Pd is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(abs Pd) . R is V11() real ext-real Element of REAL
((abs Pd) . R) " is V11() real ext-real Element of REAL
(((abs Pd) . R) ") * (abs ((y /* Pd) . R)) is V11() real ext-real Element of REAL
(abs Pd) " is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((abs Pd) ") . R is V11() real ext-real Element of REAL
(((abs Pd) ") . R) * (abs ((y /* Pd) . R)) is V11() real ext-real Element of REAL
abs (Pd ") is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(abs (Pd ")) . R is V11() real ext-real Element of REAL
((abs (Pd ")) . R) * (abs ((y /* Pd) . R)) is V11() real ext-real Element of REAL
(Pd ") . R is V11() real ext-real Element of REAL
abs ((Pd ") . R) is V11() real ext-real Element of REAL
(abs ((Pd ") . R)) * (abs ((y /* Pd) . R)) is V11() real ext-real Element of REAL
((Pd ") . R) * ((y /* Pd) . R) is V11() real ext-real Element of REAL
abs (((Pd ") . R) * ((y /* Pd) . R)) is V11() real ext-real Element of REAL
((Pd ") (#) (y /* Pd)) . R is V11() real ext-real Element of REAL
(((Pd ") (#) (y /* Pd)) . R) - 0 is V11() real ext-real Element of REAL
abs ((((Pd ") (#) (y /* Pd)) . R) - 0) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
(Pd . R) - 0 is V11() real ext-real Element of REAL
abs ((Pd . R) - 0) is V11() real ext-real Element of REAL
r is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total V158( REAL-NS 1, REAL-NS 1) V159( REAL-NS 1, REAL-NS 1) Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i * r is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of (REAL-NS 1),REAL))
K7( the carrier of (REAL-NS 1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of (REAL-NS 1),REAL)) is set
(i * r) * n is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
g is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
i * g is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(i * g) * n is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (i * g) is Element of K6((REAL 1))
y is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
y . 1 is V11() real ext-real Element of REAL
Pd is V11() real ext-real Element of REAL
dom ((i * g) * n) is V165() V166() V167() Element of K6(REAL)
dom g is Element of K6((REAL 1))
n . 1 is V40(1) Element of REAL 1
f is V11() real ext-real Element of REAL
y . f is V11() real ext-real Element of REAL
Pd * f is V11() real ext-real Element of REAL
dom n is V165() V166() V167() Element of K6(REAL)
f * 1 is V11() real ext-real Element of REAL
n . (f * 1) is V40(1) Element of REAL 1
(i * r) . (n . (f * 1)) is V11() real ext-real Element of REAL
x is Element of the carrier of (REAL-NS 1)
f * x is Element of the carrier of (REAL-NS 1)
(i * r) . (f * x) is V11() real ext-real Element of REAL
r . (f * x) is Element of the carrier of (REAL-NS 1)
i . (r . (f * x)) is V11() real ext-real Element of REAL
r . x is Element of the carrier of (REAL-NS 1)
f * (r . x) is Element of the carrier of (REAL-NS 1)
i . (f * (r . x)) is V11() real ext-real Element of REAL
i . (r . x) is V11() real ext-real Element of REAL
f * (i . (r . x)) is V11() real ext-real Element of REAL
(i * g) . (n . 1) is V11() real ext-real Element of REAL
f * ((i * g) . (n . 1)) is V11() real ext-real Element of REAL
n is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
i is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
r is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
n * r is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
(n * r) * i is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
g is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
n * g is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(n * g) * i is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K7(NAT, the carrier of (REAL-NS 1)) is set
K6(K7(NAT, the carrier of (REAL-NS 1))) is set
y is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
Pd is non empty Relation-like NAT -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total non-zero 0. (REAL-NS 1) -convergent Element of K6(K7(NAT, the carrier of (REAL-NS 1)))
y /* Pd is non empty Relation-like NAT -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of (REAL-NS 1)))
||.Pd.|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.Pd.|| " is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(||.Pd.|| ") (#) (y /* Pd) is non empty Relation-like NAT -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7(NAT, the carrier of (REAL-NS 1)))
lim ((||.Pd.|| ") (#) (y /* Pd)) is Element of the carrier of (REAL-NS 1)
lim Pd is Element of the carrier of (REAL-NS 1)
x is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
f is V11() real ext-real set
One is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Pd . I is Element of the carrier of (REAL-NS 1)
(Pd . I) - (0. (REAL-NS 1)) is Element of the carrier of (REAL-NS 1)
||.((Pd . I) - (0. (REAL-NS 1))).|| is V11() real ext-real Element of REAL
||.(Pd . I).|| is V11() real ext-real Element of REAL
x . I is V11() real ext-real Element of REAL
i . (Pd . I) is V11() real ext-real Element of REAL
(x . I) - 0 is V11() real ext-real Element of REAL
abs ((x . I) - 0) is V11() real ext-real Element of REAL
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
x . I is V11() real ext-real Element of REAL
(x . I) - 0 is V11() real ext-real Element of REAL
abs ((x . I) - 0) is V11() real ext-real Element of REAL
lim x is V11() real ext-real Element of REAL
f is set
One is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
x . One is V11() real ext-real Element of REAL
abs (x . One) is V11() real ext-real Element of REAL
Pd . One is Element of the carrier of (REAL-NS 1)
||.(Pd . One).|| is V11() real ext-real Element of REAL
i . (Pd . One) is V11() real ext-real Element of REAL
x . f is V11() real ext-real Element of REAL
i * n is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of K6(K7(REAL,REAL))
rng Pd is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
x is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Pd . x is Element of the carrier of (REAL-NS 1)
f is non empty Relation-like non-empty NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
r /* f is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(r /* f) . x is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
r . (f . x) is V11() real ext-real Element of REAL
i . (Pd . x) is V11() real ext-real Element of REAL
r . (i . (Pd . x)) is V11() real ext-real Element of REAL
g . (i . (Pd . x)) is V11() real ext-real Element of REAL
(i * n) . (g . (i . (Pd . x))) is V11() real ext-real Element of REAL
g * i is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(g * i) . (Pd . x) is V11() real ext-real Element of REAL
(i * n) . ((g * i) . (Pd . x)) is V11() real ext-real Element of REAL
n . ((g * i) . (Pd . x)) is V40(1) Element of REAL 1
i . (n . ((g * i) . (Pd . x))) is V11() real ext-real Element of REAL
n * (g * i) is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
(n * (g * i)) . (Pd . x) is set
i . ((n * (g * i)) . (Pd . x)) is V11() real ext-real Element of REAL
dom Pd is V165() V166() V167() V168() V169() V170() Element of K6(NAT)
y . (Pd . x) is set
One is Relation-like Function-like set
Pd (#) One is Relation-like Function-like set
(Pd (#) One) . x is set
dom y is Element of K6( the carrier of (REAL-NS 1))
(y /* Pd) . x is Element of the carrier of (REAL-NS 1)
i . ((y /* Pd) . x) is V11() real ext-real Element of REAL
||.(Pd . x).|| is V11() real ext-real Element of REAL
||.((||.Pd.|| ") (#) (y /* Pd)).|| is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
||.((||.Pd.|| ") (#) (y /* Pd)).|| . x is V11() real ext-real Element of REAL
((||.Pd.|| ") (#) (y /* Pd)) . x is Element of the carrier of (REAL-NS 1)
||.(((||.Pd.|| ") (#) (y /* Pd)) . x).|| is V11() real ext-real Element of REAL
(||.Pd.|| ") . x is V11() real ext-real Element of REAL
((||.Pd.|| ") . x) * ((y /* Pd) . x) is Element of the carrier of (REAL-NS 1)
||.(((||.Pd.|| ") . x) * ((y /* Pd) . x)).|| is V11() real ext-real Element of REAL
abs ((||.Pd.|| ") . x) is V11() real ext-real Element of REAL
||.((y /* Pd) . x).|| is V11() real ext-real Element of REAL
(abs ((||.Pd.|| ") . x)) * ||.((y /* Pd) . x).|| is V11() real ext-real Element of REAL
||.Pd.|| . x is V11() real ext-real Element of REAL
(||.Pd.|| . x) " is V11() real ext-real Element of REAL
abs ((||.Pd.|| . x) ") is V11() real ext-real Element of REAL
(abs ((||.Pd.|| . x) ")) * ||.((y /* Pd) . x).|| is V11() real ext-real Element of REAL
||.(Pd . x).|| " is V11() real ext-real Element of REAL
abs (||.(Pd . x).|| ") is V11() real ext-real Element of REAL
(abs (||.(Pd . x).|| ")) * ||.((y /* Pd) . x).|| is V11() real ext-real Element of REAL
(||.(Pd . x).|| ") * ||.((y /* Pd) . x).|| is V11() real ext-real Element of REAL
abs (f . x) is V11() real ext-real Element of REAL
(abs (f . x)) " is V11() real ext-real Element of REAL
((abs (f . x)) ") * ||.((y /* Pd) . x).|| is V11() real ext-real Element of REAL
abs ((r /* f) . x) is V11() real ext-real Element of REAL
((abs (f . x)) ") * (abs ((r /* f) . x)) is V11() real ext-real Element of REAL
abs (r /* f) is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(abs (r /* f)) . x is V11() real ext-real Element of REAL
((abs (f . x)) ") * ((abs (r /* f)) . x) is V11() real ext-real Element of REAL
abs f is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(abs f) . x is V11() real ext-real Element of REAL
((abs f) . x) " is V11() real ext-real Element of REAL
(((abs f) . x) ") * ((abs (r /* f)) . x) is V11() real ext-real Element of REAL
(abs f) " is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((abs f) ") . x is V11() real ext-real Element of REAL
(((abs f) ") . x) * ((abs (r /* f)) . x) is V11() real ext-real Element of REAL
((abs f) ") (#) (abs (r /* f)) is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((abs f) ") (#) (abs (r /* f))) . x is V11() real ext-real Element of REAL
f " is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
abs (f ") is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(abs (f ")) (#) (abs (r /* f)) is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((abs (f ")) (#) (abs (r /* f))) . x is V11() real ext-real Element of REAL
(f ") (#) (r /* f) is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
abs ((f ") (#) (r /* f)) is non empty Relation-like NAT -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(abs ((f ") (#) (r /* f))) . x is V11() real ext-real Element of REAL
lim ((f ") (#) (r /* f)) is V11() real ext-real Element of REAL
lim (abs ((f ") (#) (r /* f))) is V11() real ext-real Element of REAL
abs (lim ((f ") (#) (r /* f))) is V11() real ext-real Element of REAL
One is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
I is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
||.((||.Pd.|| ") (#) (y /* Pd)).|| . x is V11() real ext-real Element of REAL
(||.((||.Pd.|| ") (#) (y /* Pd)).|| . x) - 0 is V11() real ext-real Element of REAL
abs ((||.((||.Pd.|| ") (#) (y /* Pd)).|| . x) - 0) is V11() real ext-real Element of REAL
((||.Pd.|| ") (#) (y /* Pd)) . x is Element of the carrier of (REAL-NS 1)
||.(((||.Pd.|| ") (#) (y /* Pd)) . x).|| is V11() real ext-real Element of REAL
abs ||.(((||.Pd.|| ") (#) (y /* Pd)) . x).|| is V11() real ext-real Element of REAL
(((||.Pd.|| ") (#) (y /* Pd)) . x) - (0. (REAL-NS 1)) is Element of the carrier of (REAL-NS 1)
||.((((||.Pd.|| ") (#) (y /* Pd)) . x) - (0. (REAL-NS 1))).|| is V11() real ext-real Element of REAL
r is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n * r is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
(n * r) * i is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
g is V11() real ext-real Element of REAL
abs g is V11() real ext-real Element of REAL
y is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
n * y is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(n * y) * i is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
x is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
dom x is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
dom y is V165() V166() V167() Element of K6(REAL)
One is Element of the carrier of (REAL-NS 1)
i . One is V11() real ext-real Element of REAL
r . (i . One) is V11() real ext-real Element of REAL
n . (r . (i . One)) is V40(1) Element of REAL 1
(n * r) . (i . One) is set
x . One is Element of the carrier of (REAL-NS 1)
f is Element of the carrier of (REAL-NS 1)
f + One is Element of the carrier of (REAL-NS 1)
x . (f + One) is Element of the carrier of (REAL-NS 1)
i . (f + One) is V11() real ext-real Element of REAL
(n * r) . (i . (f + One)) is set
i . f is V11() real ext-real Element of REAL
(i . f) + (i . One) is V11() real ext-real Element of REAL
(n * r) . ((i . f) + (i . One)) is set
r . ((i . f) + (i . One)) is V11() real ext-real Element of REAL
n . (r . ((i . f) + (i . One))) is V40(1) Element of REAL 1
g * ((i . f) + (i . One)) is V11() real ext-real Element of REAL
n . (g * ((i . f) + (i . One))) is V40(1) Element of REAL 1
g * (i . f) is V11() real ext-real Element of REAL
g * (i . One) is V11() real ext-real Element of REAL
(g * (i . f)) + (g * (i . One)) is V11() real ext-real Element of REAL
n . ((g * (i . f)) + (g * (i . One))) is V40(1) Element of REAL 1
r . (i . f) is V11() real ext-real Element of REAL
(r . (i . f)) + (g * (i . One)) is V11() real ext-real Element of REAL
n . ((r . (i . f)) + (g * (i . One))) is V40(1) Element of REAL 1
(r . (i . f)) + (r . (i . One)) is V11() real ext-real Element of REAL
n . ((r . (i . f)) + (r . (i . One))) is V40(1) Element of REAL 1
n . (r . (i . f)) is V40(1) Element of REAL 1
(n * r) . (i . f) is set
x . f is Element of the carrier of (REAL-NS 1)
(x . f) + (x . One) is Element of the carrier of (REAL-NS 1)
f is Element of the carrier of (REAL-NS 1)
One is V11() real ext-real Element of REAL
One * f is Element of the carrier of (REAL-NS 1)
x . (One * f) is Element of the carrier of (REAL-NS 1)
i . (One * f) is V11() real ext-real Element of REAL
(n * r) . (i . (One * f)) is set
i . f is V11() real ext-real Element of REAL
One * (i . f) is V11() real ext-real Element of REAL
(n * r) . (One * (i . f)) is set
r . (One * (i . f)) is V11() real ext-real Element of REAL
n . (r . (One * (i . f))) is V40(1) Element of REAL 1
g * (One * (i . f)) is V11() real ext-real Element of REAL
n . (g * (One * (i . f))) is V40(1) Element of REAL 1
g * (i . f) is V11() real ext-real Element of REAL
One * (g * (i . f)) is V11() real ext-real Element of REAL
n . (One * (g * (i . f))) is V40(1) Element of REAL 1
r . (i . f) is V11() real ext-real Element of REAL
One * (r . (i . f)) is V11() real ext-real Element of REAL
n . (One * (r . (i . f))) is V40(1) Element of REAL 1
n . (r . (i . f)) is V40(1) Element of REAL 1
(n * r) . (i . f) is set
x . f is Element of the carrier of (REAL-NS 1)
One * (x . f) is Element of the carrier of (REAL-NS 1)
One is Element of the carrier of (REAL-NS 1)
i . One is V11() real ext-real Element of REAL
r . (i . One) is V11() real ext-real Element of REAL
n . (r . (i . One)) is V40(1) Element of REAL 1
(n * r) . (i . One) is set
f is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total V158( REAL-NS 1, REAL-NS 1) V159( REAL-NS 1, REAL-NS 1) Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
f . One is Element of the carrier of (REAL-NS 1)
||.(f . One).|| is V11() real ext-real Element of REAL
abs (r . (i . One)) is V11() real ext-real Element of REAL
g * (i . One) is V11() real ext-real Element of REAL
abs (g * (i . One)) is V11() real ext-real Element of REAL
abs (i . One) is V11() real ext-real Element of REAL
(abs g) * (abs (i . One)) is V11() real ext-real Element of REAL
||.One.|| is V11() real ext-real Element of REAL
(abs g) * ||.One.|| is V11() real ext-real Element of REAL
n is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
i (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) (i (#) ((1,1) ")) is Relation-like Function-like set
r is Element of the carrier of (REAL-NS 1)
diff (n,r) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)))
K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K228( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),(0. (REAL-NS 1))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS 1))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
(diff (n,r)) (#) (1,1) is Relation-like Function-like complex-valued ext-real-valued real-valued set
((1,1) ") (#) ((diff (n,r)) (#) (1,1)) is Relation-like Function-like complex-valued ext-real-valued real-valued set
(((1,1) ") (#) ((diff (n,r)) (#) (1,1))) . 1 is V11() real ext-real Element of REAL
g is V11() real ext-real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
diff (i,g) is V11() real ext-real Element of REAL
rng i is V165() V166() V167() Element of K6(REAL)
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
dom I is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
Pd is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total V158( REAL-NS 1, REAL-NS 1) V159( REAL-NS 1, REAL-NS 1) Lipschitzian Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(1,1) * Pd is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of (REAL-NS 1),REAL))
K7( the carrier of (REAL-NS 1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of (REAL-NS 1),REAL)) is set
((1,1) * Pd) * I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom n is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
n /. r is Element of the carrier of (REAL-NS 1)
f is Neighbourhood of r
One is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of (REAL-NS 1) : not One <= ||.(b₁ - r).|| } is set
x is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like RestFunc-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
x is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like RestFunc-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
x is set
R is Element of the carrier of (REAL-NS 1)
R - r is Element of the carrier of (REAL-NS 1)
||.(R - r).|| is V11() real ext-real Element of REAL
{ b₁ where b₁ is V11() real ext-real Element of REAL : not One <= abs (b₁ - g) } is set
x is Neighbourhood of r
L is set
y is V11() real ext-real Element of REAL
y - g is V11() real ext-real Element of REAL
abs (y - g) is V11() real ext-real Element of REAL
I . y is V40(1) Element of REAL 1
I . g is V40(1) Element of REAL 1
y0 is Element of the carrier of (REAL-NS 1)
y0 - r is Element of the carrier of (REAL-NS 1)
I . (y - g) is V40(1) Element of REAL 1
||.(y0 - r).|| is V11() real ext-real Element of REAL
(1,1) . y0 is V11() real ext-real Element of REAL
(1,1) .: x is V165() V166() V167() Element of K6(REAL)
y is set
(1,1) . y is V11() real ext-real Element of REAL
y0 is Element of the carrier of (REAL-NS 1)
y0 - r is Element of the carrier of (REAL-NS 1)
||.(y0 - r).|| is V11() real ext-real Element of REAL
(1,1) . y0 is V11() real ext-real Element of REAL
(1,1) . r is V11() real ext-real Element of REAL
(1,1) . (y0 - r) is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 - g is V11() real ext-real Element of REAL
abs (p1 - g) is V11() real ext-real Element of REAL
I * i is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
dom (I * i) is V165() V166() V167() Element of K6(REAL)
(1,1) " (dom (I * i)) is Element of K6((REAL 1))
(1,1) .: (dom n) is V165() V166() V167() Element of K6(REAL)
dom i is V165() V166() V167() Element of K6(REAL)
(1,1) " (dom i) is Element of K6((REAL 1))
(1,1) .: ((1,1) " (dom i)) is V165() V166() V167() Element of K6(REAL)
I * (1,1) is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
id (REAL 1) is non empty Relation-like REAL 1 -defined REAL 1 -valued Function-like one-to-one total quasi_total Element of K6(K7((REAL 1),(REAL 1)))
(1,1) * x is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of (REAL-NS 1),REAL))
((1,1) * x) * I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(1,1) * I is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of K6(K7(REAL,REAL))
g - One is V11() real ext-real Element of REAL
g + One is V11() real ext-real Element of REAL
].(g - One),(g + One).[ is V165() V166() V167() Element of K6(REAL)
y is set
y0 is V11() real ext-real Element of REAL
y0 - g is V11() real ext-real Element of REAL
abs (y0 - g) is V11() real ext-real Element of REAL
y is set
y0 is V11() real ext-real Element of REAL
y0 - g is V11() real ext-real Element of REAL
abs (y0 - g) is V11() real ext-real Element of REAL
(I * (1,1)) .: x is Element of K6((REAL 1))
I .: { b₁ where b₁ is V11() real ext-real Element of REAL : not One <= abs (b₁ - g) } is Element of K6((REAL 1))
i . g is V11() real ext-real Element of REAL
x is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y is V11() real ext-real Element of REAL
i . y is V11() real ext-real Element of REAL
(i . y) - (i . g) is V11() real ext-real Element of REAL
y - g is V11() real ext-real Element of REAL
x . (y - g) is V11() real ext-real Element of REAL
L . (y - g) is V11() real ext-real Element of REAL
(x . (y - g)) + (L . (y - g)) is V11() real ext-real Element of REAL
I . y is V40(1) Element of REAL 1
dom x is Element of K6( the carrier of (REAL-NS 1))
dom (((1,1) * x) * I) is V165() V166() V167() Element of K6(REAL)
x * I is Relation-like REAL -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7(REAL, the carrier of (REAL-NS 1)))
K7(REAL, the carrier of (REAL-NS 1)) is set
K6(K7(REAL, the carrier of (REAL-NS 1))) is set
(1,1) * (x * I) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom ((1,1) * (x * I)) is V165() V166() V167() Element of K6(REAL)
I . (y - g) is V40(1) Element of REAL 1
x /. (I . (y - g)) is Element of the carrier of (REAL-NS 1)
(1,1) . (x /. (I . (y - g))) is V11() real ext-real Element of REAL
x . (I . (y - g)) is set
(1,1) . (x . (I . (y - g))) is V11() real ext-real Element of REAL
(x * I) . (y - g) is set
(1,1) . ((x * I) . (y - g)) is V11() real ext-real Element of REAL
p1 is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
((1,1) * (x * I)) . (y - g) is V11() real ext-real Element of REAL
dom (((1,1) * Pd) * I) is V165() V166() V167() Element of K6(REAL)
Pd * I is Relation-like REAL -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7(REAL, the carrier of (REAL-NS 1)))
(1,1) * (Pd * I) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom ((1,1) * (Pd * I)) is V165() V166() V167() Element of K6(REAL)
n /. (I . y) is Element of the carrier of (REAL-NS 1)
(1,1) . (n /. (I . y)) is V11() real ext-real Element of REAL
n . (I . y) is set
(1,1) . (n . (I . y)) is V11() real ext-real Element of REAL
n * I is Relation-like REAL -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7(REAL, the carrier of (REAL-NS 1)))
(n * I) . y is set
(1,1) . ((n * I) . y) is V11() real ext-real Element of REAL
p1 is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(1,1) * n is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of (REAL-NS 1),REAL))
i * (1,1) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
I * (i * (1,1)) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(1,1) * (I * (i * (1,1))) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(id REAL) * (i * (1,1)) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
rng (i * (1,1)) is V165() V166() V167() Element of K6(REAL)
((1,1) * n) * I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i * (1,1)) * I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
i * (id REAL) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(1,1) * (n * I) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom ((1,1) * (n * I)) is V165() V166() V167() Element of K6(REAL)
((1,1) * (n * I)) . y is V11() real ext-real Element of REAL
n /. (I . g) is Element of the carrier of (REAL-NS 1)
(1,1) . (n /. (I . g)) is V11() real ext-real Element of REAL
n . (I . g) is set
(1,1) . (n . (I . g)) is V11() real ext-real Element of REAL
(n * I) . g is set
(1,1) . ((n * I) . g) is V11() real ext-real Element of REAL
p1 is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
((1,1) * (n * I)) . g is V11() real ext-real Element of REAL
y0 is Element of the carrier of (REAL-NS 1)
n /. y0 is Element of the carrier of (REAL-NS 1)
(n /. y0) - (n /. r) is Element of the carrier of (REAL-NS 1)
(1,1) . ((n /. y0) - (n /. r)) is V11() real ext-real Element of REAL
y0 - r is Element of the carrier of (REAL-NS 1)
Pd . (y0 - r) is Element of the carrier of (REAL-NS 1)
x /. (y0 - r) is Element of the carrier of (REAL-NS 1)
(Pd . (y0 - r)) + (x /. (y0 - r)) is Element of the carrier of (REAL-NS 1)
(1,1) . ((Pd . (y0 - r)) + (x /. (y0 - r))) is V11() real ext-real Element of REAL
(1,1) . (n /. y0) is V11() real ext-real Element of REAL
(1,1) . (n /. r) is V11() real ext-real Element of REAL
((1,1) . (n /. y0)) - ((1,1) . (n /. r)) is V11() real ext-real Element of REAL
((1,1) . (n /. (I . y))) - ((1,1) . (n /. (I . g))) is V11() real ext-real Element of REAL
(1,1) . (Pd . (y0 - r)) is V11() real ext-real Element of REAL
(1,1) . (x /. (y0 - r)) is V11() real ext-real Element of REAL
((1,1) . (Pd . (y0 - r))) + ((1,1) . (x /. (y0 - r))) is V11() real ext-real Element of REAL
Pd . (I . (y - g)) is set
(1,1) . (Pd . (I . (y - g))) is V11() real ext-real Element of REAL
((1,1) . (Pd . (I . (y - g)))) + ((1,1) . (x /. (y0 - r))) is V11() real ext-real Element of REAL
(Pd * I) . (y - g) is set
(1,1) . ((Pd * I) . (y - g)) is V11() real ext-real Element of REAL
p1 is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
((1,1) * (Pd * I)) . (y - g) is V11() real ext-real Element of REAL
<*1*> is Relation-like NAT -defined NAT -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued natural-valued FinSequence of NAT
n is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
i (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) (i (#) ((1,1) ")) is Relation-like Function-like set
r is Element of the carrier of (REAL-NS 1)
diff (n,r) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)))
K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K228( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),(0. (REAL-NS 1))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS 1))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
(diff (n,r)) . <*1*> is set
g is V11() real ext-real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
diff (i,g) is V11() real ext-real Element of REAL
<*(diff (i,g))*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
Pd is V11() real ext-real Element of REAL
dom i is V165() V166() V167() Element of K6(REAL)
diff (i,Pd) is V11() real ext-real Element of REAL
i . Pd is V11() real ext-real Element of REAL
x is V165() V166() V167() Neighbourhood of Pd
f is V11() real ext-real set
Pd - f is V11() real ext-real Element of REAL
Pd + f is V11() real ext-real Element of REAL
].(Pd - f),(Pd + f).[ is V165() V166() V167() Element of K6(REAL)
One is V11() real ext-real Element of REAL
{ b₁ where b₁ is Element of the carrier of (REAL-NS 1) : not One <= ||.(b₁ - r).|| } is set
i * (1,1) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
rng (i * (1,1)) is V165() V166() V167() Element of K6(REAL)
I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
I . 1 is V11() real ext-real Element of REAL
x is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
I . 1 is V11() real ext-real Element of REAL
x is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
I * x is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
(I * x) * (1,1) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
I * I is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
(I * I) * (1,1) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
dom n is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
rng I is Element of K6((REAL 1))
y is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(1,1) * I is non empty Relation-like REAL -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
id REAL is non empty Relation-like REAL -defined REAL -valued Function-like one-to-one total quasi_total complex-valued ext-real-valued real-valued increasing non-decreasing Element of K6(K7(REAL,REAL))
y is set
y0 is Element of the carrier of (REAL-NS 1)
y0 - r is Element of the carrier of (REAL-NS 1)
||.(y0 - r).|| is V11() real ext-real Element of REAL
(1,1) . y0 is V11() real ext-real Element of REAL
(1,1) . r is V11() real ext-real Element of REAL
(1,1) . (y0 - r) is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
p1 - Pd is V11() real ext-real Element of REAL
abs (p1 - Pd) is V11() real ext-real Element of REAL
I . p1 is V40(1) Element of REAL 1
I .: x is Element of K6((REAL 1))
y0 is set
I . y0 is set
p1 is V11() real ext-real Element of REAL
I . p1 is V40(1) Element of REAL 1
I . Pd is V40(1) Element of REAL 1
p2 is Element of the carrier of (REAL-NS 1)
p2 - r is Element of the carrier of (REAL-NS 1)
p1 - Pd is V11() real ext-real Element of REAL
I . (p1 - Pd) is V40(1) Element of REAL 1
abs (p1 - Pd) is V11() real ext-real Element of REAL
||.(p2 - r).|| is V11() real ext-real Element of REAL
(1,1) * n is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7( the carrier of (REAL-NS 1),REAL))
K7( the carrier of (REAL-NS 1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7( the carrier of (REAL-NS 1),REAL)) is set
I * (i * (1,1)) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(1,1) * (I * (i * (1,1))) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(id REAL) * (i * (1,1)) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
((1,1) * n) * I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i * (1,1)) * I is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
i * (id REAL) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom ((1,1) * n) is Element of K6( the carrier of (REAL-NS 1))
I " (dom ((1,1) * n)) is V165() V166() V167() Element of K6(REAL)
rng n is Element of K6( the carrier of (REAL-NS 1))
I .: (dom i) is Element of K6((REAL 1))
I " (dom n) is V165() V166() V167() Element of K6(REAL)
I .: (I " (dom n)) is Element of K6((REAL 1))
y is set
y0 is Element of the carrier of (REAL-NS 1)
y0 - r is Element of the carrier of (REAL-NS 1)
||.(y0 - r).|| is V11() real ext-real Element of REAL
((1,1) * I) .: x is V165() V166() V167() Element of K6(REAL)
(1,1) .: { b₁ where b₁ is Element of the carrier of (REAL-NS 1) : not One <= ||.(b₁ - r).|| } is V165() V166() V167() Element of K6(REAL)
n /. r is Element of the carrier of (REAL-NS 1)
L is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total V158( REAL-NS 1, REAL-NS 1) V159( REAL-NS 1, REAL-NS 1) Lipschitzian Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
R is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like RestFunc-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i . ((1,1) . r) is V11() real ext-real Element of REAL
I . (i . ((1,1) . r)) is V40(1) Element of REAL 1
(i * (1,1)) . r is V11() real ext-real Element of REAL
I . ((i * (1,1)) . r) is V40(1) Element of REAL 1
dom (I * (i * (1,1))) is Element of K6((REAL 1))
(I * (i * (1,1))) . r is set
n . r is set
y is Element of the carrier of (REAL-NS 1)
n /. y is Element of the carrier of (REAL-NS 1)
(n /. y) - (n /. r) is Element of the carrier of (REAL-NS 1)
y - r is Element of the carrier of (REAL-NS 1)
L . (y - r) is Element of the carrier of (REAL-NS 1)
R /. (y - r) is Element of the carrier of (REAL-NS 1)
(L . (y - r)) + (R /. (y - r)) is Element of the carrier of (REAL-NS 1)
(1,1) . y is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
i . y0 is V11() real ext-real Element of REAL
I . (i . y0) is V40(1) Element of REAL 1
I . (i . Pd) is V40(1) Element of REAL 1
y0 - Pd is V11() real ext-real Element of REAL
I . (y0 - Pd) is V11() real ext-real Element of REAL
I . (I . (y0 - Pd)) is V40(1) Element of REAL 1
x . (y0 - Pd) is V11() real ext-real Element of REAL
I . (x . (y0 - Pd)) is V40(1) Element of REAL 1
(i . y0) - (i . Pd) is V11() real ext-real Element of REAL
I . ((i . y0) - (i . Pd)) is V40(1) Element of REAL 1
(I . (y0 - Pd)) + (x . (y0 - Pd)) is V11() real ext-real Element of REAL
I . ((I . (y0 - Pd)) + (x . (y0 - Pd))) is V40(1) Element of REAL 1
p1 is Element of the carrier of (REAL-NS 1)
p2 is Element of the carrier of (REAL-NS 1)
p1 - p2 is Element of the carrier of (REAL-NS 1)
q1 is Element of the carrier of (REAL-NS 1)
q2 is Element of the carrier of (REAL-NS 1)
q1 + q2 is Element of the carrier of (REAL-NS 1)
(I . (i . y0)) - (I . (i . Pd)) is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
i . ((1,1) . y) is V11() real ext-real Element of REAL
I . (i . ((1,1) . y)) is V40(1) Element of REAL 1
(I . (i . ((1,1) . y))) - (I . (i . ((1,1) . r))) is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
(I . (I . (y0 - Pd))) + (I . (x . (y0 - Pd))) is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
(1,1) . (y - r) is V11() real ext-real Element of REAL
I . ((1,1) . (y - r)) is V11() real ext-real Element of REAL
I . (I . ((1,1) . (y - r))) is V40(1) Element of REAL 1
(I . (I . ((1,1) . (y - r)))) + (I . (x . (y0 - Pd))) is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
x . ((1,1) . (y - r)) is V11() real ext-real Element of REAL
I . (x . ((1,1) . (y - r))) is V40(1) Element of REAL 1
(I . (I . ((1,1) . (y - r)))) + (I . (x . ((1,1) . (y - r)))) is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
dom L is Element of K6( the carrier of (REAL-NS 1))
dom ((I * I) * (1,1)) is Element of K6((REAL 1))
I * (1,1) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
I * (I * (1,1)) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
dom (I * (I * (1,1))) is Element of K6((REAL 1))
x * (1,1) is Relation-like REAL 1 -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(x * (1,1)) . (y - r) is V11() real ext-real Element of REAL
I . ((x * (1,1)) . (y - r)) is V40(1) Element of REAL 1
dom ((I * x) * (1,1)) is Element of K6((REAL 1))
I * (x * (1,1)) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
dom (I * (x * (1,1))) is Element of K6((REAL 1))
(I * (x * (1,1))) . (y - r) is set
((I * x) * (1,1)) . (y - r) is set
(i * (1,1)) . y is V11() real ext-real Element of REAL
I . ((i * (1,1)) . y) is V40(1) Element of REAL 1
(I * (1,1)) . (y - r) is V11() real ext-real Element of REAL
I . ((I * (1,1)) . (y - r)) is V40(1) Element of REAL 1
(I * (I * (1,1))) . (y - r) is set
(I * (i * (1,1))) . y is set
n . y is set
dom I is V165() V166() V167() Element of K6(REAL)
I . 1 is V40(1) Element of REAL 1
((I * I) * (1,1)) . (I . 1) is set
(1,1) . (I . 1) is V11() real ext-real Element of REAL
(I * I) . ((1,1) . (I . 1)) is set
I . ((1,1) . (I . 1)) is V11() real ext-real Element of REAL
I . (I . ((1,1) . (I . 1))) is V40(1) Element of REAL 1
I . (I . 1) is V40(1) Element of REAL 1
n is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
i (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) (i (#) ((1,1) ")) is Relation-like Function-like set
r is Element of the carrier of (REAL-NS 1)
g is V11() real ext-real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
n is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
i is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
i (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) (i (#) ((1,1) ")) is Relation-like Function-like set
r is Element of the carrier of (REAL-NS 1)
diff (n,r) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)))
K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K228( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),(0. (REAL-NS 1))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS 1))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
(diff (n,r)) . <*1*> is set
g is V11() real ext-real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
diff (i,g) is V11() real ext-real Element of REAL
<*(diff (i,g))*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
y is Element of the carrier of (REAL-NS n)
(n,r,y) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
g is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
g * (n,r,y) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(r,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(r,n) . y is Element of the carrier of (REAL-NS 1)
diff ((g * (n,r,y)),((r,n) . y)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i)))
K313( the carrier of (REAL-NS 1),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS i)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))
0. (REAL-NS i) is V52( REAL-NS i) Element of the carrier of (REAL-NS i)
K228( the carrier of (REAL-NS i), the carrier of (REAL-NS 1),(0. (REAL-NS i))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS i))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS i))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS i))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS i))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS i))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS i)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS i))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))) is non empty set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,g) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
r is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
r * (n,i,g) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . g is V11() real ext-real Element of REAL
diff ((r * (n,i,g)),((i,n) . g)) is V11() real ext-real Element of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
g is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,r,g) is V11() real ext-real set
(n,i,g) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
r * (n,i,g) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . g is V11() real ext-real Element of REAL
diff ((r * (n,i,g)),((i,n) . g)) is V11() real ext-real Element of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
(i,n) (#) ((1,1) ") is Relation-like Function-like set
g is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
g is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
r is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
r * (i,n) is non empty Relation-like REAL n -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
(r * (i,n)) . g is V40(1) Element of REAL 1
(i,n) . g is V11() real ext-real Element of REAL
r . ((i,n) . g) is V40(1) Element of REAL 1
<*((i,n) . g)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(i,n) . g is set
y is Element of the carrier of (REAL-NS n)
(i,n) . y is Element of the carrier of (REAL-NS 1)
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Element of the carrier of (REAL-NS n)
(n,i,r) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
g is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,g) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
(n,i,g) * (1,1) is non empty Relation-like REAL 1 -defined REAL n -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL n)))
K7((REAL 1),(REAL n)) is set
K6(K7((REAL 1),(REAL n))) is set
Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
y is non empty Relation-like REAL 1 -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 1),REAL))
(n,i,g) * y is non empty Relation-like REAL 1 -defined REAL n -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL n)))
((n,i,g) * y) . Pd is V40(n) Element of REAL n
y . Pd is V11() real ext-real Element of REAL
(n,i,g) . (y . Pd) is V40(n) Element of REAL n
x is Element of the carrier of (REAL-NS 1)
(n,i,r) . x is Element of the carrier of (REAL-NS n)
(n,i,r) . Pd is set
f is V11() real ext-real Element of REAL
<*f*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
One is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,One) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
(n,i,One) . f is V40(n) Element of REAL n
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(n,g) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
g (#) ((1,1) ") is Relation-like Function-like set
y is Element of the carrier of (REAL-NS n)
(n,i,y) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
r * (n,i,y) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
Pd is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,Pd) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
g * (n,i,Pd) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((g * (n,i,Pd))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(g * (n,i,Pd)) (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) ((g * (n,i,Pd)) (#) ((1,1) ")) is Relation-like Function-like set
f is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(n,i,Pd) * (1,1) is non empty Relation-like REAL 1 -defined REAL n -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL n)))
K7((REAL 1),(REAL n)) is set
K6(K7((REAL 1),(REAL n))) is set
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
x * g is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
(x * g) * (n,i,Pd) is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
((x * g) * (n,i,Pd)) * (1,1) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(n,g) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
g (#) ((1,1) ") is Relation-like Function-like set
y is Element of the carrier of (REAL-NS n)
Pd is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . Pd is V11() real ext-real Element of REAL
<*((i,n) . Pd)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(i,n) . y is Element of the carrier of (REAL-NS 1)
(n,i,y) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
r * (n,i,y) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(n,i,Pd) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
g * (n,i,Pd) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((g * (n,i,Pd))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(g * (n,i,Pd)) (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) ((g * (n,i,Pd)) (#) ((1,1) ")) is Relation-like Function-like set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(n,g) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
g (#) ((1,1) ") is Relation-like Function-like set
y is Element of the carrier of (REAL-NS n)
(n,1,i,r,y) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)))
K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K228( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),(0. (REAL-NS 1))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS 1))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
(n,i,y) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
r * (n,i,y) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(i,n) . y is Element of the carrier of (REAL-NS 1)
diff ((r * (n,i,y)),((i,n) . y)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,r,y) . <*1*> is set
Pd is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,g,Pd) is V11() real ext-real Element of REAL
(n,i,Pd) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
g * (n,i,Pd) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . Pd is V11() real ext-real Element of REAL
diff ((g * (n,i,Pd)),((i,n) . Pd)) is V11() real ext-real Element of REAL
<*(n,i,g,Pd)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*((i,n) . Pd)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((g * (n,i,Pd))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(g * (n,i,Pd)) (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) ((g * (n,i,Pd)) (#) ((1,1) ")) is Relation-like Function-like set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Relation-like REAL n -defined REAL i -valued Function-like Element of K6(K7((REAL n),(REAL i)))
y is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
Pd is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
x is Element of the carrier of (REAL-NS n)
(n,i,r,Pd,x) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i)))
K313( the carrier of (REAL-NS 1),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS i)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))
0. (REAL-NS i) is V52( REAL-NS i) Element of the carrier of (REAL-NS i)
K228( the carrier of (REAL-NS i), the carrier of (REAL-NS 1),(0. (REAL-NS i))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS i))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS i))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS i))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS i))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS i))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS i)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS i))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))) is non empty set
(n,r,x) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
Pd * (n,r,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
(r,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(r,n) . x is Element of the carrier of (REAL-NS 1)
diff ((Pd * (n,r,x)),((r,n) . x)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
K7((REAL 1),(REAL i)) is set
K6(K7((REAL 1),(REAL i))) is set
(n,i,r,Pd,x) . <*1*> is set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
I is Element of the carrier of (REAL-NS n)
f is Relation-like NAT -defined REAL -valued Function-like V40(i) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL i
(n,i,r,x,I) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,r,I) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
x * (n,r,I) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
(r,n) . I is Element of the carrier of (REAL-NS 1)
diff ((x * (n,r,I)),((r,n) . I)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,i,r,x,I) . <*1*> is set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
R is Element of the carrier of (REAL-NS n)
One is Relation-like NAT -defined REAL -valued Function-like V40(i) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL i
(n,i,r,x,R) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,r,R) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
x * (n,r,R) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
(r,n) . R is Element of the carrier of (REAL-NS 1)
diff ((x * (n,r,R)),((r,n) . R)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,i,r,x,R) . <*1*> is set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
r is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS r is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS r) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r))) is set
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL r is non empty FinSequence-membered FinSequenceSet of REAL
r -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL i),(REAL r)) is set
K6(K7((REAL i),(REAL r))) is set
g is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS r) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r)))
y is Relation-like REAL i -defined REAL r -valued Function-like Element of K6(K7((REAL i),(REAL r)))
Pd is Element of the carrier of (REAL-NS i)
x is Relation-like NAT -defined REAL -valued Function-like V40(i) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL i
f is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS r) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r)))
One is Element of the carrier of (REAL-NS i)
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
r is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS r is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS r) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r))) is set
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL r is non empty FinSequence-membered FinSequenceSet of REAL
r -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL i),(REAL r)) is set
K6(K7((REAL i),(REAL r))) is set
g is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS r) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS r)))
y is Relation-like REAL i -defined REAL r -valued Function-like Element of K6(K7((REAL i),(REAL r)))
Pd is Element of the carrier of (REAL-NS i)
(i,r,n,g,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS r)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS r)))
K313( the carrier of (REAL-NS 1),(REAL-NS r)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS r)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS r)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS r) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))
0. (REAL-NS r) is V52( REAL-NS r) Element of the carrier of (REAL-NS r)
K228( the carrier of (REAL-NS r), the carrier of (REAL-NS 1),(0. (REAL-NS r))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS r) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS r)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS r)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS r))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS r))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS r))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS r))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS r)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS r))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS r)),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS r))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS r)),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS r))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS r)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS r))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS r))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS r))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS r))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))),(LinearOperators ((REAL-NS 1),(REAL-NS r))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS r)),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS r)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS r)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS r)))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS r)))),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS r)))),(LinearOperators ((REAL-NS 1),(REAL-NS r))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS r))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS r)),(LinearOperators ((REAL-NS 1),(REAL-NS r)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS r)),(LinearOperators ((REAL-NS 1),(REAL-NS r)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS r)),(LinearOperators ((REAL-NS 1),(REAL-NS r)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS r)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS r))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS r))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS r))) is non empty set
(i,n,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
g * (i,n,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS r) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS r)))
(n,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(n,i) . Pd is Element of the carrier of (REAL-NS 1)
diff ((g * (i,n,Pd)),((n,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS r)))
(i,r,n,g,Pd) . <*1*> is set
x is Relation-like NAT -defined REAL -valued Function-like V40(i) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL i
(i,r,n,y,x) is Relation-like NAT -defined REAL -valued Function-like V40(r) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL r
K7((REAL 1),(REAL r)) is set
K6(K7((REAL 1),(REAL r))) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(n,r) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
r (#) ((1,1) ") is Relation-like Function-like set
g is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
y is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
Pd is Element of the carrier of (REAL-NS n)
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(n,r) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
r (#) ((1,1) ") is Relation-like Function-like set
g is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,r,g) is V11() real ext-real Element of REAL
(n,i,g) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
r * (n,i,g) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . g is V11() real ext-real Element of REAL
diff ((r * (n,i,g)),((i,n) . g)) is V11() real ext-real Element of REAL
<*(n,i,r,g)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
y is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
(n,1,i,y,g) is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
Pd is Element of the carrier of (REAL-NS n)
(n,1,i,x,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)))
K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K228( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),(0. (REAL-NS 1))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS 1))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
(n,i,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
x * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(i,n) . Pd is Element of the carrier of (REAL-NS 1)
diff ((x * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,x,Pd) . <*1*> is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Pd is Element of the carrier of (REAL-NS n)
(n,r,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
y is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
g is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
(g,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(g,i) * y is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
((g,i) * y) * (n,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(r,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(r,n) . Pd is Element of the carrier of (REAL-NS 1)
diff ((((g,i) * y) * (n,r,Pd)),((r,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)))
K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
0. (REAL-NS 1) is V52( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K228( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),(0. (REAL-NS 1))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS 1))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
Pd is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,r,Pd) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
y is Relation-like REAL n -defined REAL i -valued Function-like Element of K6(K7((REAL n),(REAL i)))
g is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
(g,i) is non empty Relation-like REAL i -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL i),REAL))
K7((REAL i),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL i),REAL)) is set
(g,i) * y is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
((g,i) * y) * (n,r,Pd) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(r,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(r,n) . Pd is V11() real ext-real Element of REAL
diff ((((g,i) * y) * (n,r,Pd)),((r,n) . Pd)) is V11() real ext-real Element of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
r is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
g is Relation-like REAL n -defined REAL i -valued Function-like Element of K6(K7((REAL n),(REAL i)))
y is Element of the carrier of (REAL-NS n)
Pd is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
f is Element of the carrier of (REAL-NS n)
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
r is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
g is Relation-like REAL n -defined REAL i -valued Function-like Element of K6(K7((REAL n),(REAL i)))
y is Element of the carrier of (REAL-NS n)
diff (r,y) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))
R_NormSpace_of_BoundedLinearOperators ((REAL-NS n),(REAL-NS i)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS n),(REAL-NS i)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))))
R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS n),(REAL-NS i)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS n),(REAL-NS i)))
K313( the carrier of (REAL-NS n),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS n), the carrier of (REAL-NS i)
FuncZero ( the carrier of (REAL-NS n),(REAL-NS i)) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))
0. (REAL-NS i) is V52( REAL-NS i) Element of the carrier of (REAL-NS i)
K228( the carrier of (REAL-NS i), the carrier of (REAL-NS n),(0. (REAL-NS i))) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
FuncAdd ( the carrier of (REAL-NS n),(REAL-NS i)) is Relation-like K7((Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))))
K7((Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))))) is set
FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS i)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS n), the carrier of (REAL-NS i))),(FuncZero ( the carrier of (REAL-NS n),(REAL-NS i))),(FuncAdd ( the carrier of (REAL-NS n),(REAL-NS i))),(FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS i))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS n),(REAL-NS i)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS n),(REAL-NS i))) is set
K199(K313( the carrier of (REAL-NS n),(REAL-NS i)),(LinearOperators ((REAL-NS n),(REAL-NS i)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS n),(REAL-NS i))
K197(K313( the carrier of (REAL-NS n),(REAL-NS i)),(LinearOperators ((REAL-NS n),(REAL-NS i)))) is Relation-like K7((LinearOperators ((REAL-NS n),(REAL-NS i))),(LinearOperators ((REAL-NS n),(REAL-NS i)))) -defined LinearOperators ((REAL-NS n),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS n),(REAL-NS i))),(LinearOperators ((REAL-NS n),(REAL-NS i)))),(LinearOperators ((REAL-NS n),(REAL-NS i)))))
K7((LinearOperators ((REAL-NS n),(REAL-NS i))),(LinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K7(K7((LinearOperators ((REAL-NS n),(REAL-NS i))),(LinearOperators ((REAL-NS n),(REAL-NS i)))),(LinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K6(K7(K7((LinearOperators ((REAL-NS n),(REAL-NS i))),(LinearOperators ((REAL-NS n),(REAL-NS i)))),(LinearOperators ((REAL-NS n),(REAL-NS i))))) is set
K198(K313( the carrier of (REAL-NS n),(REAL-NS i)),(LinearOperators ((REAL-NS n),(REAL-NS i)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS n),(REAL-NS i)))) -defined LinearOperators ((REAL-NS n),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS n),(REAL-NS i)))),(LinearOperators ((REAL-NS n),(REAL-NS i)))))
K7(REAL,(LinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS n),(REAL-NS i)))),(LinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS n),(REAL-NS i)))),(LinearOperators ((REAL-NS n),(REAL-NS i))))) is set
RLSStruct(# (LinearOperators ((REAL-NS n),(REAL-NS i))),K199(K313( the carrier of (REAL-NS n),(REAL-NS i)),(LinearOperators ((REAL-NS n),(REAL-NS i)))),K197(K313( the carrier of (REAL-NS n),(REAL-NS i)),(LinearOperators ((REAL-NS n),(REAL-NS i)))),K198(K313( the carrier of (REAL-NS n),(REAL-NS i)),(LinearOperators ((REAL-NS n),(REAL-NS i)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is Element of BoundedLinearOperators ((REAL-NS n),(REAL-NS i))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS n),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))))
K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS n),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i))))) is set
BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS i)) is non empty Relation-like BoundedLinearOperators ((REAL-NS n),(REAL-NS i)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),REAL))
K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS n),(REAL-NS i))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS n),(REAL-NS i)))),(BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS i))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS n),(REAL-NS i))) is non empty set
Pd is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,g,Pd) is non empty Relation-like REAL n -defined REAL i -valued Function-like total quasi_total Element of K6(K7((REAL n),(REAL i)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),(REAL i)) is set
K6(K7((REAL n),(REAL i))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
(r,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(r,i) is non empty Relation-like REAL i -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL i),REAL))
K7((REAL i),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL i),REAL)) is set
g is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
y is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
(r,i) * y is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
Pd is Relation-like REAL n -defined REAL i -valued Function-like Element of K6(K7((REAL n),(REAL i)))
(r,i) * Pd is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
x is Element of the carrier of (REAL-NS n)
(n,g,x) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
((r,i) * y) * (n,g,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
f is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,g,f) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
((r,i) * Pd) * (n,g,f) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((((r,i) * Pd) * (n,g,f))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(((r,i) * Pd) * (n,g,f)) (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) ((((r,i) * Pd) * (n,g,f)) (#) ((1,1) ")) is Relation-like Function-like set
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
Pd * (n,g,f) is Relation-like REAL -defined REAL i -valued Function-like Element of K6(K7(REAL,(REAL i)))
K7(REAL,(REAL i)) is set
K6(K7(REAL,(REAL i))) is set
(r,i) * (Pd * (n,g,f)) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
One is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
One * ((r,i) * (Pd * (n,g,f))) is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
(One * ((r,i) * (Pd * (n,g,f)))) * (1,1) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
One * (r,i) is non empty Relation-like REAL i -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7((REAL i),(REAL 1)))
K7((REAL i),(REAL 1)) is set
K6(K7((REAL i),(REAL 1))) is set
(One * (r,i)) * (Pd * (n,g,f)) is Relation-like REAL -defined REAL 1 -valued Function-like Element of K6(K7(REAL,(REAL 1)))
((One * (r,i)) * (Pd * (n,g,f))) * (1,1) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(Pd * (n,g,f)) * (1,1) is Relation-like REAL 1 -defined REAL i -valued Function-like Element of K6(K7((REAL 1),(REAL i)))
K7((REAL 1),(REAL i)) is set
K6(K7((REAL 1),(REAL i))) is set
(One * (r,i)) * ((Pd * (n,g,f)) * (1,1)) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(n,g,f) * (1,1) is non empty Relation-like REAL 1 -defined REAL n -valued Function-like total quasi_total Element of K6(K7((REAL 1),(REAL n)))
K7((REAL 1),(REAL n)) is set
K6(K7((REAL 1),(REAL n))) is set
Pd * ((n,g,f) * (1,1)) is Relation-like REAL 1 -defined REAL i -valued Function-like Element of K6(K7((REAL 1),(REAL i)))
(One * (r,i)) * (Pd * ((n,g,f) * (1,1))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(r,i) * (Pd * ((n,g,f) * (1,1))) is Relation-like REAL 1 -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7((REAL 1), the carrier of (REAL-NS 1)))
K7((REAL 1), the carrier of (REAL-NS 1)) is set
K6(K7((REAL 1), the carrier of (REAL-NS 1))) is set
Pd * (n,g,x) is Relation-like the carrier of (REAL-NS 1) -defined REAL i -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1),(REAL i)))
K7( the carrier of (REAL-NS 1),(REAL i)) is set
K6(K7( the carrier of (REAL-NS 1),(REAL i))) is set
(r,i) * (Pd * (n,g,x)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL i),(REAL n)) is set
K6(K7((REAL i),(REAL n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Relation-like REAL i -defined REAL n -valued Function-like Element of K6(K7((REAL i),(REAL n)))
x is Element of the carrier of (REAL-NS i)
f is Relation-like NAT -defined REAL -valued Function-like V40(i) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL i
(r,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(r,i) . x is Element of the carrier of (REAL-NS 1)
(r,i) is non empty Relation-like REAL i -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL i),REAL))
K7((REAL i),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL i),REAL)) is set
(r,i) . f is V11() real ext-real Element of REAL
<*((r,i) . f)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(i,r,x) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(g,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(g,n) * y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
((g,n) * y) * (i,r,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(i,r,f) is non empty Relation-like REAL -defined REAL i -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL i)))
K7(REAL,(REAL i)) is set
K6(K7(REAL,(REAL i))) is set
(g,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
(g,n) * Pd is Relation-like REAL i -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL i),REAL))
((g,n) * Pd) * (i,r,f) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((((g,n) * Pd) * (i,r,f))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(((g,n) * Pd) * (i,r,f)) (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) ((((g,n) * Pd) * (i,r,f)) (#) ((1,1) ")) is Relation-like Function-like set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
REAL i is non empty FinSequence-membered FinSequenceSet of REAL
i -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL i),(REAL n)) is set
K6(K7((REAL i),(REAL n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Relation-like REAL i -defined REAL n -valued Function-like Element of K6(K7((REAL i),(REAL n)))
x is Element of the carrier of (REAL-NS i)
(i,n,r,g,y,x) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(i,r,x) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(g,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(g,n) * y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
((g,n) * y) * (i,r,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(r,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
(r,i) . x is Element of the carrier of (REAL-NS 1)
diff ((((g,n) * y) * (i,r,x)),((r,i) . x)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(i,n,r,g,y,x) . <*1*> is set
f is Relation-like NAT -defined REAL -valued Function-like V40(i) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL i
(i,n,r,g,Pd,f) is V11() real ext-real set
(i,r,f) is non empty Relation-like REAL -defined REAL i -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL i)))
K7(REAL,(REAL i)) is set
K6(K7(REAL,(REAL i))) is set
(g,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
(g,n) * Pd is Relation-like REAL i -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL i),REAL))
K7((REAL i),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL i),REAL)) is set
((g,n) * Pd) * (i,r,f) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(r,i) is non empty Relation-like REAL i -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL i),REAL))
(r,i) . f is V11() real ext-real Element of REAL
diff ((((g,n) * Pd) * (i,r,f)),((r,i) . f)) is V11() real ext-real Element of REAL
<*(i,n,r,g,Pd,f)*> is Relation-like Function-like set
<*((r,i) . f)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
((((g,n) * Pd) * (i,r,f))) is Relation-like REAL 1 -defined REAL 1 -valued Function-like Element of K6(K7((REAL 1),(REAL 1)))
(((g,n) * Pd) * (i,r,f)) (#) ((1,1) ") is Relation-like Function-like set
(1,1) (#) ((((g,n) * Pd) * (i,r,f)) (#) ((1,1) ")) is Relation-like Function-like set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
K6( the carrier of (REAL-NS i)) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is set
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
dom y is Element of K6( the carrier of (REAL-NS i))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS i)))
y is set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS i)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i)))
K313( the carrier of (REAL-NS 1),(REAL-NS i)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS i)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))
0. (REAL-NS i) is V52( REAL-NS i) Element of the carrier of (REAL-NS i)
K228( the carrier of (REAL-NS i), the carrier of (REAL-NS 1),(0. (REAL-NS i))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS i)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS i))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS i))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS i))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS i))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS i))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS i))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS i)))),(LinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS i))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS i)),(LinearOperators ((REAL-NS 1),(REAL-NS i)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS i)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS i))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS i))) #) is strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))) is non empty set
K7( the carrier of (REAL-NS n), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))))) is set
Pd is Relation-like the carrier of (REAL-NS n) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
dom Pd is Element of K6( the carrier of (REAL-NS n))
K6( the carrier of (REAL-NS n)) is set
x is set
x is set
x is Element of the carrier of (REAL-NS n)
Pd . x is set
(n,i,r,g,x) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,r,x) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
g * (n,r,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
(r,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(r,n) . x is Element of the carrier of (REAL-NS 1)
diff ((g * (n,r,x)),((r,n) . x)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
Pd /. x is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
Pd is Relation-like the carrier of (REAL-NS n) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
dom Pd is Element of K6( the carrier of (REAL-NS n))
K6( the carrier of (REAL-NS n)) is set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i))) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))))
dom x is Element of K6( the carrier of (REAL-NS n))
f is Element of the carrier of (REAL-NS n)
Pd /. f is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,i,r,g,f) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
(n,r,f) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
g * (n,r,f) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
(r,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(r,n) . f is Element of the carrier of (REAL-NS 1)
diff ((g * (n,r,f)),((r,n) . f)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
x /. f is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS i)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
g + y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
g - y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Element of the carrier of (REAL-NS i)
(i,r,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(g + y) * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
g * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
y * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(g * (i,r,Pd)) + (y * (i,r,Pd)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(g - y) * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(g * (i,r,Pd)) - (y * (i,r,Pd)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
dom (i,r,Pd) is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
dom (g + y) is Element of K6( the carrier of (REAL-NS i))
K6( the carrier of (REAL-NS i)) is set
dom g is Element of K6( the carrier of (REAL-NS i))
dom y is Element of K6( the carrier of (REAL-NS i))
(dom g) /\ (dom y) is Element of K6( the carrier of (REAL-NS i))
dom ((g + y) * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom ((g * (i,r,Pd)) + (y * (i,r,Pd))) is Element of K6( the carrier of (REAL-NS 1))
x is Element of the carrier of (REAL-NS 1)
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
dom (g * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom (y * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
(dom (g * (i,r,Pd))) /\ (dom (y * (i,r,Pd))) is Element of K6( the carrier of (REAL-NS 1))
x is set
f is set
x is Element of the carrier of (REAL-NS 1)
((g + y) * (i,r,Pd)) . x is set
((g * (i,r,Pd)) + (y * (i,r,Pd))) . x is set
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
dom (g * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom (y * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
y /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
y . ((i,r,Pd) . x) is set
(y * (i,r,Pd)) . x is set
(y * (i,r,Pd)) /. x is Element of the carrier of (REAL-NS n)
g /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
g . ((i,r,Pd) . x) is set
(g * (i,r,Pd)) . x is set
(g * (i,r,Pd)) /. x is Element of the carrier of (REAL-NS n)
(g + y) . ((i,r,Pd) . x) is set
(g + y) /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
(g /. ((i,r,Pd) . x)) + (y /. ((i,r,Pd) . x)) is Element of the carrier of (REAL-NS n)
((g * (i,r,Pd)) + (y * (i,r,Pd))) /. x is Element of the carrier of (REAL-NS n)
dom (g - y) is Element of K6( the carrier of (REAL-NS i))
dom ((g - y) * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom ((g * (i,r,Pd)) - (y * (i,r,Pd))) is Element of K6( the carrier of (REAL-NS 1))
x is Element of the carrier of (REAL-NS 1)
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
dom (g * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom (y * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
(dom (g * (i,r,Pd))) /\ (dom (y * (i,r,Pd))) is Element of K6( the carrier of (REAL-NS 1))
x is set
f is set
x is Element of the carrier of (REAL-NS 1)
((g - y) * (i,r,Pd)) . x is set
((g * (i,r,Pd)) - (y * (i,r,Pd))) . x is set
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
dom (g * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom (y * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
y /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
y . ((i,r,Pd) . x) is set
(y * (i,r,Pd)) . x is set
(y * (i,r,Pd)) /. x is Element of the carrier of (REAL-NS n)
g /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
g . ((i,r,Pd) . x) is set
(g * (i,r,Pd)) . x is set
(g * (i,r,Pd)) /. x is Element of the carrier of (REAL-NS n)
(g - y) . ((i,r,Pd) . x) is set
(g - y) /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
(g /. ((i,r,Pd) . x)) - (y /. ((i,r,Pd) . x)) is Element of the carrier of (REAL-NS n)
((g * (i,r,Pd)) - (y * (i,r,Pd))) /. x is Element of the carrier of (REAL-NS n)
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is V11() real ext-real Element of REAL
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
g (#) y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Element of the carrier of (REAL-NS i)
(i,r,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
y * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
g (#) (y * (i,r,Pd)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(g (#) y) * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
dom (g (#) y) is Element of K6( the carrier of (REAL-NS i))
K6( the carrier of (REAL-NS i)) is set
dom y is Element of K6( the carrier of (REAL-NS i))
dom (g (#) (y * (i,r,Pd))) is Element of K6( the carrier of (REAL-NS 1))
K6( the carrier of (REAL-NS 1)) is set
dom (y * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
dom (i,r,Pd) is Element of K6( the carrier of (REAL-NS 1))
dom ((g (#) y) * (i,r,Pd)) is Element of K6( the carrier of (REAL-NS 1))
x is Element of the carrier of (REAL-NS 1)
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
x is set
f is set
x is Element of the carrier of (REAL-NS 1)
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
x is Element of the carrier of (REAL-NS 1)
(g (#) (y * (i,r,Pd))) . x is set
((g (#) y) * (i,r,Pd)) . x is set
(i,r,Pd) . x is Element of the carrier of (REAL-NS i)
y /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
y . ((i,r,Pd) . x) is set
(y * (i,r,Pd)) . x is set
(y * (i,r,Pd)) /. x is Element of the carrier of (REAL-NS n)
(g (#) (y * (i,r,Pd))) /. x is Element of the carrier of (REAL-NS n)
g * (y /. ((i,r,Pd) . x)) is Element of the carrier of (REAL-NS n)
(g (#) y) . ((i,r,Pd) . x) is set
(g (#) y) /. ((i,r,Pd) . x) is Element of the carrier of (REAL-NS n)
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n)))
K313( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS n)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))
0. (REAL-NS n) is V52( REAL-NS n) Element of the carrier of (REAL-NS n)
K228( the carrier of (REAL-NS n), the carrier of (REAL-NS 1),(0. (REAL-NS n))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS n))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS n))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS n))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n))) #) is strict NORMSTR
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
g + y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Element of the carrier of (REAL-NS i)
(i,n,r,(g + y),Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) is non empty set
(i,r,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(g + y) * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(r,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(r,i) . Pd is Element of the carrier of (REAL-NS 1)
diff (((g + y) * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,g,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
g * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff ((g * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,y,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
y * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff ((y * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,g,Pd) + (i,n,r,y,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(g * (i,r,Pd)) + (y * (i,r,Pd)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff (((g * (i,r,Pd)) + (y * (i,r,Pd))),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
r + g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
y is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,(r + g),y) is V11() real ext-real Element of REAL
(n,i,y) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
(r + g) * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . y is V11() real ext-real Element of REAL
diff (((r + g) * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,r,y) is V11() real ext-real Element of REAL
r * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((r * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,g,y) is V11() real ext-real Element of REAL
g * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,r,y) + (n,i,g,y) is V11() real ext-real Element of REAL
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(n,r) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
r (#) ((1,1) ") is Relation-like Function-like set
(n,g) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
g (#) ((1,1) ") is Relation-like Function-like set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
Pd is Element of the carrier of (REAL-NS n)
(n,1,i,x,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,i,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
x * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(i,n) . Pd is Element of the carrier of (REAL-NS 1)
diff ((x * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
One is Element of the carrier of (REAL-NS 1)
(n,1,i,x,Pd) . One is Element of the carrier of (REAL-NS 1)
<*(n,i,r,y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*(n,i,g,y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
rng g is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
dom (g (#) ((1,1) ")) is set
dom g is Element of K6((REAL n))
K6((REAL n)) is set
rng r is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
dom (r (#) ((1,1) ")) is set
dom r is Element of K6((REAL n))
f is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
x + f is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
dom (x + f) is Element of K6( the carrier of (REAL-NS n))
K6( the carrier of (REAL-NS n)) is set
(dom r) /\ (dom g) is Element of K6((REAL n))
dom (r + g) is Element of K6((REAL n))
rng (r + g) is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(r + g) (#) ((1,1) ") is Relation-like Function-like set
dom ((r + g) (#) ((1,1) ")) is set
x is Element of the carrier of (REAL-NS n)
(x + f) . x is set
(x + f) /. x is Element of the carrier of (REAL-NS 1)
x /. x is Element of the carrier of (REAL-NS 1)
f /. x is Element of the carrier of (REAL-NS 1)
(x /. x) + (f /. x) is Element of the carrier of (REAL-NS 1)
dom x is Element of K6( the carrier of (REAL-NS n))
dom f is Element of K6( the carrier of (REAL-NS n))
(dom x) /\ (dom f) is Element of K6( the carrier of (REAL-NS n))
(r (#) ((1,1) ")) . x is set
(g (#) ((1,1) ")) . x is set
g . x is V11() real ext-real Element of REAL
((1,1) ") . (g . x) is set
r . x is V11() real ext-real Element of REAL
((1,1) ") . (r . x) is set
(n,(r + g)) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
(n,(r + g)) . x is set
(r + g) . x is V11() real ext-real Element of REAL
((1,1) ") . ((r + g) . x) is set
(r . x) + (g . x) is V11() real ext-real Element of REAL
((1,1) ") . ((r . x) + (g . x)) is set
R is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(n,1,i,f,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
f * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff ((f * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,f,Pd) . One is Element of the carrier of (REAL-NS 1)
dom (n,(r + g)) is Element of K6((REAL n))
<*(n,i,(r + g),y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,1,i,(x + f),Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(x + f) * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff (((x + f) * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,(x + f),Pd) . <*1*> is set
(n,1,i,x,Pd) + (n,1,i,f,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
((n,1,i,x,Pd) + (n,1,i,f,Pd)) . <*1*> is set
((n,1,i,x,Pd) . One) + ((n,1,i,f,Pd) . One) is Element of the carrier of (REAL-NS 1)
I is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
x is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
I + x is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*((n,i,r,y) + (n,i,g,y))*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*((n,i,r,y) + (n,i,g,y))*> . 1 is V11() real ext-real Element of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n)))
K313( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS n)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))
0. (REAL-NS n) is V52( REAL-NS n) Element of the carrier of (REAL-NS n)
K228( the carrier of (REAL-NS n), the carrier of (REAL-NS 1),(0. (REAL-NS n))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS n))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS n))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS n))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n))) #) is strict NORMSTR
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
g - y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Element of the carrier of (REAL-NS i)
(i,n,r,(g - y),Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) is non empty set
(i,r,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(g - y) * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(r,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(r,i) . Pd is Element of the carrier of (REAL-NS 1)
diff (((g - y) * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,g,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
g * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff ((g * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,y,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
y * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff ((y * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,g,Pd) - (i,n,r,y,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(g * (i,r,Pd)) - (y * (i,r,Pd)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff (((g * (i,r,Pd)) - (y * (i,r,Pd))),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
r - g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
y is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,(r - g),y) is V11() real ext-real Element of REAL
(n,i,y) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
(r - g) * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . y is V11() real ext-real Element of REAL
diff (((r - g) * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,r,y) is V11() real ext-real Element of REAL
r * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((r * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,g,y) is V11() real ext-real Element of REAL
g * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,r,y) - (n,i,g,y) is V11() real ext-real Element of REAL
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(n,r) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
r (#) ((1,1) ") is Relation-like Function-like set
(n,g) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
g (#) ((1,1) ") is Relation-like Function-like set
x is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
Pd is Element of the carrier of (REAL-NS n)
(n,1,i,x,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,i,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
x * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(i,n) . Pd is Element of the carrier of (REAL-NS 1)
diff ((x * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
One is Element of the carrier of (REAL-NS 1)
(n,1,i,x,Pd) . One is Element of the carrier of (REAL-NS 1)
<*(n,i,r,y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*(n,i,g,y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
rng g is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
dom (g (#) ((1,1) ")) is set
dom g is Element of K6((REAL n))
K6((REAL n)) is set
rng r is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
dom (r (#) ((1,1) ")) is set
dom r is Element of K6((REAL n))
f is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
x - f is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
dom (x - f) is Element of K6( the carrier of (REAL-NS n))
K6( the carrier of (REAL-NS n)) is set
(dom r) /\ (dom g) is Element of K6((REAL n))
dom (r - g) is Element of K6((REAL n))
rng (r - g) is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(r - g) (#) ((1,1) ") is Relation-like Function-like set
dom ((r - g) (#) ((1,1) ")) is set
x is Element of the carrier of (REAL-NS n)
(x - f) . x is set
(x - f) /. x is Element of the carrier of (REAL-NS 1)
x /. x is Element of the carrier of (REAL-NS 1)
f /. x is Element of the carrier of (REAL-NS 1)
(x /. x) - (f /. x) is Element of the carrier of (REAL-NS 1)
dom x is Element of K6( the carrier of (REAL-NS n))
dom f is Element of K6( the carrier of (REAL-NS n))
(dom x) /\ (dom f) is Element of K6( the carrier of (REAL-NS n))
(r (#) ((1,1) ")) . x is set
(g (#) ((1,1) ")) . x is set
g . x is V11() real ext-real Element of REAL
((1,1) ") . (g . x) is set
r . x is V11() real ext-real Element of REAL
((1,1) ") . (r . x) is set
(n,(r - g)) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
(n,(r - g)) . x is set
(r - g) . x is V11() real ext-real Element of REAL
((1,1) ") . ((r - g) . x) is set
(r . x) - (g . x) is V11() real ext-real Element of REAL
((1,1) ") . ((r . x) - (g . x)) is set
R is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(n,1,i,f,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
f * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff ((f * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,f,Pd) . One is Element of the carrier of (REAL-NS 1)
dom (n,(r - g)) is Element of K6((REAL n))
<*(n,i,(r - g),y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,1,i,(x - f),Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(x - f) * (n,i,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff (((x - f) * (n,i,Pd)),((i,n) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,(x - f),Pd) . <*1*> is set
(n,1,i,x,Pd) - (n,1,i,f,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
((n,1,i,x,Pd) - (n,1,i,f,Pd)) . <*1*> is set
((n,1,i,x,Pd) . One) - ((n,1,i,f,Pd) . One) is Element of the carrier of (REAL-NS 1)
I is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
x is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
I - x is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*((n,i,r,y) - (n,i,g,y))*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*((n,i,r,y) - (n,i,g,y))*> . 1 is V11() real ext-real Element of REAL
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() RealNormSpace-like V161() NORMSTR
BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty Element of K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty functional Element of K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n)))
K313( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is non empty functional FUNCTION_DOMAIN of the carrier of (REAL-NS 1), the carrier of (REAL-NS n)
FuncZero ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))
0. (REAL-NS n) is V52( REAL-NS n) Element of the carrier of (REAL-NS n)
K228( the carrier of (REAL-NS n), the carrier of (REAL-NS 1),(0. (REAL-NS n))) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))))
K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K6(K7(K7((Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))) is set
FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS n)) is Relation-like K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) -defined Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))))
K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is set
K6(K7(K7(REAL,(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))),(Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))) is set
RLSStruct(# (Funcs ( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),(FuncZero ( the carrier of (REAL-NS 1),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS 1),(REAL-NS n))) #) is strict RLSStruct
the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty set
K6( the carrier of K313( the carrier of (REAL-NS 1),(REAL-NS n))) is set
K199(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS 1),(REAL-NS n))
K197(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K198(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS n))),K199(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K197(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K198(K313( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) #) is V71() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))) is non empty set
K6( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))
K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like total quasi_total Element of K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K6(K7(K7(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n)) is non empty Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is set
NORMSTR(# (BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),K199((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K197((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K198((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n))) #) is strict NORMSTR
i is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL-NS i is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS i) is non empty V2() set
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n))) is set
r is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
g is V11() real ext-real Element of REAL
y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
g (#) y is Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS n)))
Pd is Element of the carrier of (REAL-NS i)
(i,n,r,(g (#) y),Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) is non empty set
(i,r,Pd) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS i) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS i))) is set
(g (#) y) * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(r,i) is non empty Relation-like the carrier of (REAL-NS i) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)))
K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS i), the carrier of (REAL-NS 1))) is set
(r,i) . Pd is Element of the carrier of (REAL-NS 1)
diff (((g (#) y) * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(i,n,r,y,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
y * (i,r,Pd) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff ((y * (i,r,Pd)),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
g * (i,n,r,y,Pd) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
g (#) (y * (i,r,Pd)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
diff ((g (#) (y * (i,r,Pd))),((r,i) . Pd)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
REAL n is non empty FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is FinSequence-membered FinSequenceSet of REAL
K7((REAL n),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL n),REAL)) is set
i is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V139() V164() V165() V166() V167() V168() V169() V170() Element of NAT
r is V11() real ext-real Element of REAL
g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
r (#) g is Relation-like REAL n -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
y is Relation-like NAT -defined REAL -valued Function-like V40(n) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL n
(n,i,(r (#) g),y) is V11() real ext-real Element of REAL
(n,i,y) is non empty Relation-like REAL -defined REAL n -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL n)))
K7(REAL,(REAL n)) is set
K6(K7(REAL,(REAL n))) is set
(r (#) g) * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(i,n) is non empty Relation-like REAL n -defined REAL -valued Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL n),REAL))
(i,n) . y is V11() real ext-real Element of REAL
diff (((r (#) g) * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
(n,i,g,y) is V11() real ext-real Element of REAL
g * (n,i,y) is Relation-like REAL -defined REAL -valued Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g * (n,i,y)),((i,n) . y)) is V11() real ext-real Element of REAL
r * (n,i,g,y) is V11() real ext-real Element of REAL
REAL-NS n is non empty V50() V71() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() V107() strict RealNormSpace-like V161() NORMSTR
the carrier of (REAL-NS n) is non empty V2() set
rng g is V165() V166() V167() Element of K6(REAL)
Pd is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
g (#) ((1,1) ") is Relation-like Function-like set
dom (g (#) ((1,1) ")) is set
dom g is Element of K6((REAL n))
K6((REAL n)) is set
<*(n,i,g,y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(n,g) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
K7((REAL n),(REAL 1)) is set
K6(K7((REAL n),(REAL 1))) is set
f is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
x is Element of the carrier of (REAL-NS n)
r (#) f is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
dom (r (#) f) is Element of K6( the carrier of (REAL-NS n))
K6( the carrier of (REAL-NS n)) is set
dom (r (#) g) is Element of K6((REAL n))
rng (r (#) g) is V165() V166() V167() Element of K6(REAL)
x is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
(r (#) g) (#) ((1,1) ") is Relation-like Function-like set
dom ((r (#) g) (#) ((1,1) ")) is set
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
I is non empty Relation-like REAL -defined REAL 1 -valued Function-like total quasi_total Element of K6(K7(REAL,(REAL 1)))
x is Element of the carrier of (REAL-NS n)
(n,(r (#) g)) is Relation-like REAL n -defined REAL 1 -valued Function-like Element of K6(K7((REAL n),(REAL 1)))
(n,(r (#) g)) . x is set
(r (#) g) . x is V11() real ext-real Element of REAL
((1,1) ") . ((r (#) g) . x) is set
(r (#) f) . x is set
(r (#) f) /. x is Element of the carrier of (REAL-NS 1)
f /. x is Element of the carrier of (REAL-NS 1)
r * (f /. x) is Element of the carrier of (REAL-NS 1)
dom f is Element of K6( the carrier of (REAL-NS n))
(g (#) ((1,1) ")) . x is set
g . x is V11() real ext-real Element of REAL
((1,1) ") . (g . x) is set
r * (g . x) is V11() real ext-real Element of REAL
I . (r * (g . x)) is V40(1) Element of REAL 1
(n,1,i,f,x) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,i,x) is non empty Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
f * (n,i,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
(i,n) is non empty Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like total quasi_total Element of K6(K7( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(i,n) . x is Element of the carrier of (REAL-NS 1)
diff ((f * (n,i,x)),((i,n) . x)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
One is Element of the carrier of (REAL-NS 1)
(n,1,i,f,x) . One is Element of the carrier of (REAL-NS 1)
dom (n,(r (#) g)) is Element of K6((REAL n))
<*(n,i,(r (#) g),y)*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
(n,1,i,(r (#) f),x) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(r (#) f) * (n,i,x) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K6(K7( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff (((r (#) f) * (n,i,x)),((i,n) . x)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(n,1,i,(r (#) f),x) . <*1*> is set
r * (n,1,i,f,x) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(r * (n,1,i,f,x)) . <*1*> is set
r * ((n,1,i,f,x) . One) is Element of the carrier of (REAL-NS 1)
Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
r * Pd is Relation-like NAT -defined REAL -valued Function-like V40(1) FinSequence-like complex-valued ext-real-valued real-valued Element of REAL 1
<*(r * (n,i,g,y))*> is Relation-like NAT -defined REAL -valued Function-like FinSequence-like complex-valued ext-real-valued real-valued FinSequence of REAL
<*(r * (n,i,g,y))*> . 1 is V11() real ext-real Element of REAL