REAL is non empty non finite complex-membered ext-real-membered real-membered V66() non bounded_below non bounded_above V76() set
NAT is non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below Element of K10(REAL)
K10(REAL) is non finite set
COMPLEX is non empty non finite complex-membered V66() set
RAT is non empty non finite complex-membered ext-real-membered real-membered rational-membered V66() set
INT is non empty non finite complex-membered ext-real-membered real-membered rational-membered integer-membered V66() set
K11(COMPLEX,COMPLEX) is complex-yielding non finite set
K10(K11(COMPLEX,COMPLEX)) is non finite set
K11(K11(COMPLEX,COMPLEX),COMPLEX) is complex-yielding non finite set
K10(K11(K11(COMPLEX,COMPLEX),COMPLEX)) is non finite set
K11(REAL,REAL) is complex-yielding V37() V38() non finite set
K10(K11(REAL,REAL)) is non finite set
K11(K11(REAL,REAL),REAL) is complex-yielding V37() V38() non finite set
K10(K11(K11(REAL,REAL),REAL)) is non finite set
K11(RAT,RAT) is RAT -valued complex-yielding V37() V38() non finite set
K10(K11(RAT,RAT)) is non finite set
K11(K11(RAT,RAT),RAT) is RAT -valued complex-yielding V37() V38() non finite set
K10(K11(K11(RAT,RAT),RAT)) is non finite set
K11(INT,INT) is RAT -valued INT -valued complex-yielding V37() V38() non finite set
K10(K11(INT,INT)) is non finite set
K11(K11(INT,INT),INT) is RAT -valued INT -valued complex-yielding V37() V38() non finite set
K10(K11(K11(INT,INT),INT)) is non finite set
K11(NAT,NAT) is RAT -valued INT -valued complex-yielding V37() V38() V39() non finite set
K11(K11(NAT,NAT),NAT) is RAT -valued INT -valued complex-yielding V37() V38() V39() non finite set
K10(K11(K11(NAT,NAT),NAT)) is non finite set
NAT is non empty V12() V13() V14() non finite V53() V54() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() left_end bounded_below set
K10(NAT) is non finite set
K10(NAT) is non finite set
K11(COMPLEX,REAL) is complex-yielding V37() V38() non finite set
K10(K11(COMPLEX,REAL)) is non finite set
K455() is non empty V109() L8()
the carrier of K455() is non empty set
K460() is non empty V109() V131() V132() V133() V135() V161() V162() V163() V164() V165() V166() L8()
K461() is non empty V109() V133() V135() V164() V165() V166() M17(K460())
K462() is non empty V109() V131() V133() V135() V164() V165() V166() V167() M20(K460(),K461())
K464() is non empty V109() V131() V133() V135() L8()
K465() is non empty V109() V131() V133() V135() V167() M17(K464())
K11(NAT,REAL) is complex-yielding V37() V38() non finite set
K10(K11(NAT,REAL)) is non finite set
K496() is non empty set
K11(K496(),K496()) is set
K11(K11(K496(),K496()),K496()) is set
K10(K11(K11(K496(),K496()),K496())) is set
K11(REAL,K496()) is non finite set
K11(K11(REAL,K496()),K496()) is non finite set
K10(K11(K11(REAL,K496()),K496())) is non finite set
K502() is RLSStruct
the carrier of K502() is set
K10( the carrier of K502()) is set
K506() is Element of K10( the carrier of K502())
K11(K506(),K506()) is set
K11(K11(K506(),K506()),REAL) is complex-yielding V37() V38() set
K10(K11(K11(K506(),K506()),REAL)) is set
K509() is Element of K10( the carrier of K502())
K11(K509(),REAL) is complex-yielding V37() V38() set
K10(K11(K509(),REAL)) is set
1 is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
K11(1,1) is RAT -valued INT -valued complex-yielding V37() V38() V39() set
K10(K11(1,1)) is set
K11(K11(1,1),1) is RAT -valued INT -valued complex-yielding V37() V38() V39() set
K10(K11(K11(1,1),1)) is set
K11(K11(1,1),REAL) is complex-yielding V37() V38() set
K10(K11(K11(1,1),REAL)) is set
2 is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
K11(2,2) is RAT -valued INT -valued complex-yielding V37() V38() V39() set
K11(K11(2,2),REAL) is complex-yielding V37() V38() set
K10(K11(K11(2,2),REAL)) is set
TOP-REAL 2 is non empty V107() V151() V152() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital TopSpace-like V226() L20()
the carrier of (TOP-REAL 2) is non empty set
REAL 1 is non empty functional FinSequence-membered FinSequenceSet of REAL
1 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
K11((REAL 1),(REAL 1)) is set
K10(K11((REAL 1),(REAL 1))) is set
REAL-NS 1 is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS 1) is non empty V2() set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) is non empty Element of K10( 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 V107() V151() 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 K10( the carrier of K517( the carrier of (REAL-NS 1),(REAL-NS 1)))
K517( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is non empty M4( 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 V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))
K401((REAL-NS 1)) is V88( REAL-NS 1) Element of the carrier of (REAL-NS 1)
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS 1),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( 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 K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( 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 K517( the carrier of (REAL-NS 1),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS 1),(REAL-NS 1))) is set
K505(K517( 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))
K503(K517( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K11((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 V32(K11((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))), LinearOperators ((REAL-NS 1),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS 1))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))), LinearOperators ((REAL-NS 1),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),(LinearOperators ((REAL-NS 1),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS 1),(REAL-NS 1)),(LinearOperators ((REAL-NS 1),(REAL-NS 1)))) #) is V107() 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
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K505((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))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K11((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 V32(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))),K504((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 V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is non empty set
{} is set
the empty V12() V13() V14() V16() V17() V18() V19() real ext-real non positive non negative Function-like functional finite V53() V55( {} ) FinSequence-membered complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() bounded_below bounded_above real-bounded V76() set is empty V12() V13() V14() V16() V17() V18() V19() real ext-real non positive non negative Function-like functional finite V53() V55( {} ) FinSequence-membered complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() bounded_below bounded_above real-bounded V76() set
3 is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
0 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
m is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
TOP-REAL m is non empty V107() V151() V152() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital TopSpace-like V226() L20()
the carrier of (TOP-REAL m) is non empty set
n is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Seg m is finite V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= m ) } is set
f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
|.f.| is V19() real ext-real non negative Element of REAL
sqr f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr f) is V19() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V19() real ext-real Element of REAL
X is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of the carrier of (TOP-REAL m)
X /. n is V19() real ext-real Element of REAL
abs (X /. n) is V19() real ext-real Element of REAL
0* m is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
m |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of m -tuples_on REAL
(X /. n) ^2 is V19() real ext-real Element of REAL
K69((X /. n),(X /. n)) is V19() real ext-real set
(0* m) +* (n,((X /. n) ^2)) is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum ((0* m) +* (n,((X /. n) ^2))) is V19() real ext-real Element of REAL
len (0* m) is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
len ((0* m) +* (n,((X /. n) ^2))) is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
i is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of m -tuples_on REAL
len i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
sqr f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of m -tuples_on REAL
Sum (sqr f) is V19() real ext-real Element of REAL
len f is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
j is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of m -tuples_on REAL
r is V12() V13() V14() V18() V19() real ext-real non negative finite V53() set
i . r is V19() real ext-real Element of REAL
j . r is V19() real ext-real Element of REAL
dom f is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
f /. r is V19() real ext-real Element of REAL
f . r is V19() real ext-real Element of REAL
dom (0* m) is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
Seg (len (0* m)) is finite V55( len (0* m)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= len (0* m) ) } is set
dom i is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
i /. n is V19() real ext-real Element of REAL
f /. n is V19() real ext-real Element of REAL
(f /. n) ^2 is V19() real ext-real Element of REAL
K69((f /. n),(f /. n)) is V19() real ext-real set
dom (0* m) is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
Seg (len (0* m)) is finite V55( len (0* m)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= len (0* m) ) } is set
dom f is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
f /. r is V19() real ext-real Element of REAL
f . r is V19() real ext-real Element of REAL
(f /. r) ^2 is V19() real ext-real Element of REAL
K69((f /. r),(f /. r)) is V19() real ext-real set
dom i is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
i /. r is V19() real ext-real Element of REAL
(0* m) /. r is V19() real ext-real Element of REAL
m |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-yielding V37() V38() V39() finite V55(m) FinSequence-like FinSubsequence-like Element of m -tuples_on NAT
m -tuples_on NAT is non empty functional FinSequence-membered FinSequenceSet of NAT
(m |-> 0) . r is empty V12() V13() V14() V16() V17() V18() V19() real ext-real non positive non negative Function-like functional finite V53() V55( {} ) FinSequence-membered complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() bounded_below bounded_above real-bounded V76() Element of REAL
Sum i is V19() real ext-real Element of REAL
Sum j is V19() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V19() real ext-real Element of REAL
(sqrt (Sum (sqr f))) ^2 is V19() real ext-real Element of REAL
K69((sqrt (Sum (sqr f))),(sqrt (Sum (sqr f)))) is V19() real ext-real set
sqrt ((X /. n) ^2) is V19() real ext-real Element of REAL
sqrt ((sqrt (Sum (sqr f))) ^2) is V19() real ext-real Element of REAL
abs (abs (X /. n)) is V19() real ext-real Element of REAL
abs (sqrt (Sum (sqr f))) is V19() real ext-real Element of REAL
m is V19() real ext-real Element of REAL
<*m*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,m] is set
{[1,m]} is non empty V2() Function-like V55(1) set
abs m is V19() real ext-real Element of REAL
n is Element of the carrier of (REAL-NS 1)
||.n.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . n is V19() real ext-real Element of REAL
f is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like Element of REAL 1
sqr f is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like Element of 1 -tuples_on REAL
Sum (sqr f) is V19() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V19() real ext-real Element of REAL
m ^2 is V19() real ext-real Element of REAL
K69(m,m) is V19() real ext-real set
<*(m ^2)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(m ^2)] is set
{[1,(m ^2)]} is non empty V2() Function-like V55(1) set
Sum <*(m ^2)*> is V19() real ext-real Element of REAL
sqrt (Sum <*(m ^2)*>) is V19() real ext-real Element of REAL
sqrt (m ^2) is V19() real ext-real Element of REAL
|.f.| is V19() real ext-real non negative Element of REAL
sqr f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr f) is V19() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
n is Element of the carrier of (REAL-NS m)
||.n.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . n is V19() real ext-real Element of REAL
f is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (f,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
(Proj (f,m)) . n is Element of the carrier of (REAL-NS 1)
||.((Proj (f,m)) . n).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . ((Proj (f,m)) . n) is V19() real ext-real Element of REAL
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
X is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
|.X.| is V19() real ext-real non negative Element of REAL
sqr X is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr X) is V19() real ext-real Element of REAL
sqrt (Sum (sqr X)) is V19() real ext-real Element of REAL
proj (f,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (f,m)) . n is V19() real ext-real Element of REAL
<*((proj (f,m)) . n)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (f,m)) . n)] is set
{[1,((proj (f,m)) . n)]} is non empty V2() Function-like V55(1) set
X . f is V19() real ext-real Element of REAL
<*(X . f)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(X . f)] is set
{[1,(X . f)]} is non empty V2() Function-like V55(1) set
abs (X . f) is V19() real ext-real Element of REAL
TOP-REAL m is non empty V107() V151() V152() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital TopSpace-like V226() L20()
the carrier of (TOP-REAL m) is non empty set
Seg m is non empty finite V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= m ) } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of the carrier of (TOP-REAL m)
i /. f is V19() real ext-real Element of REAL
abs (i /. f) is V19() real ext-real Element of REAL
dom X is V55(m) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
n is Element of the carrier of (REAL-NS m)
f is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (f,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
(Proj (f,m)) . n is Element of the carrier of (REAL-NS 1)
||.((Proj (f,m)) . n).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . ((Proj (f,m)) . n) is V19() real ext-real Element of REAL
proj (f,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (f,m)) . n is V19() real ext-real Element of REAL
|.((proj (f,m)) . n).| is V19() real ext-real Element of REAL
<*((proj (f,m)) . n)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (f,m)) . n)] is set
{[1,((proj (f,m)) . n)]} is non empty V2() Function-like V55(1) set
X is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
X . f is V19() real ext-real Element of REAL
<*(X . f)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(X . f)] is set
{[1,(X . f)]} is non empty V2() Function-like V55(1) set
abs (X . f) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
|.n.| is V19() real ext-real non negative Element of REAL
sqr n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr n) is V19() real ext-real Element of REAL
sqrt (Sum (sqr n)) is V19() real ext-real Element of REAL
f is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
proj (f,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (f,m)) . n is V19() real ext-real Element of REAL
|.((proj (f,m)) . n).| is V19() real ext-real Element of REAL
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
Proj (f,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
X is Element of the carrier of (REAL-NS m)
(Proj (f,m)) . X is Element of the carrier of (REAL-NS 1)
||.((Proj (f,m)) . X).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . ((Proj (f,m)) . X) is V19() real ext-real Element of REAL
(proj (f,m)) . X is V19() real ext-real Element of REAL
|.((proj (f,m)) . X).| is V19() real ext-real Element of REAL
||.X.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . X is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL))
BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1)))
K517( the carrier of (REAL-NS n),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS n),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS n),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS n),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS n),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS n),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))), LinearOperators ((REAL-NS n),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS n),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))), LinearOperators ((REAL-NS n),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS n),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) #) is V107() 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 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL)) is non finite set
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (X,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS 1))) . (Proj (X,n)) is V19() real ext-real Element of REAL
i is Element of the carrier of (REAL-NS n)
j is V19() real ext-real Element of REAL
j * i is Element of the carrier of (REAL-NS n)
(Proj (X,n)) . (j * i) is Element of the carrier of (REAL-NS 1)
(Proj (X,n)) . i is Element of the carrier of (REAL-NS 1)
j * ((Proj (X,n)) . i) is Element of the carrier of (REAL-NS 1)
i is Element of the carrier of (REAL-NS n)
j is Element of the carrier of (REAL-NS n)
i + j is Element of the carrier of (REAL-NS n)
(Proj (X,n)) . (i + j) is Element of the carrier of (REAL-NS 1)
(Proj (X,n)) . i is Element of the carrier of (REAL-NS 1)
(Proj (X,n)) . j is Element of the carrier of (REAL-NS 1)
((Proj (X,n)) . i) + ((Proj (X,n)) . j) is Element of the carrier of (REAL-NS 1)
modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) V149( REAL-NS n, REAL-NS 1) homogeneous Lipschitzian Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
PreNorms (modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))) is non empty complex-membered ext-real-membered real-membered Element of K10(REAL)
{ ||.((modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))) . b1).|| where b1 is Element of the carrier of (REAL-NS n) : ||.b1.|| <= 1 } is set
upper_bound (PreNorms (modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1)))) is V19() real ext-real Element of REAL
j is V19() real ext-real set
r is Element of the carrier of (REAL-NS n)
(modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))) . r is Element of the carrier of (REAL-NS 1)
||.((modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))) . r).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . ((modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))) . r) is V19() real ext-real Element of REAL
||.r.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) is Relation-like the carrier of (REAL-NS n) -defined REAL -valued Function-like V32( the carrier of (REAL-NS n), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS n),REAL))
K11( the carrier of (REAL-NS n),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS n),REAL)) is non finite set
the U9 of (REAL-NS n) . r is V19() real ext-real Element of REAL
(Proj (X,n)) . r is Element of the carrier of (REAL-NS 1)
||.((Proj (X,n)) . r).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) . ((Proj (X,n)) . r) is V19() real ext-real Element of REAL
j is ext-real set
(upper_bound (PreNorms (modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))))) - 1 is V19() real ext-real Element of REAL
(upper_bound (PreNorms (modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))))) - ((upper_bound (PreNorms (modetrans ((Proj (X,n)),(REAL-NS n),(REAL-NS 1))))) - 1) is V19() real ext-real Element of REAL
r is V19() real ext-real set
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL))
BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1)))
K517( the carrier of (REAL-NS n),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS n),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS n),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS n),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS n),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS n),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))), LinearOperators ((REAL-NS n),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS n),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))), LinearOperators ((REAL-NS n),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS n),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) #) is V107() 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 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL)) is non finite set
f is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n))) . f is V19() real ext-real Element of REAL
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (X,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
f * (Proj (X,n)) is Relation-like Function-like set
(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1))) . (f * (Proj (X,n))) is V19() real ext-real Element of REAL
(BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS 1))) . (Proj (X,n)) is V19() real ext-real Element of REAL
((BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS 1))) . (Proj (X,n))) * ((BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n))) . f) is V19() real ext-real Element of REAL
H1(m,1) . (f * (Proj (X,n))) is V19() real ext-real Element of REAL
H1(n,1) . (Proj (X,n)) is V19() real ext-real Element of REAL
H1(m,n) . f is V19() real ext-real Element of REAL
(H1(n,1) . (Proj (X,n))) * (H1(m,n) . f) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (n,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
the carrier of (REAL-NS m) is non empty V2() set
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
f is Element of the carrier of (REAL-NS m)
X is V19() real ext-real Element of REAL
X * f is Element of the carrier of (REAL-NS m)
(Proj (n,m)) . (X * f) is Element of the carrier of (REAL-NS 1)
(Proj (n,m)) . f is Element of the carrier of (REAL-NS 1)
X * ((Proj (n,m)) . f) is Element of the carrier of (REAL-NS 1)
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
f is V19() real ext-real Element of REAL
f * n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
proj (X,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (X,m)) . (f * n) is V19() real ext-real Element of REAL
(proj (X,m)) . n is V19() real ext-real Element of REAL
f * ((proj (X,m)) . n) is V19() real ext-real Element of REAL
(f * n) . X is V19() real ext-real Element of REAL
n . X is V19() real ext-real Element of REAL
f * (n . X) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
n + f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
proj (X,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (X,m)) . (n + f) is V19() real ext-real Element of REAL
(proj (X,m)) . n is V19() real ext-real Element of REAL
(proj (X,m)) . f is V19() real ext-real Element of REAL
((proj (X,m)) . n) + ((proj (X,m)) . f) is V19() real ext-real Element of REAL
(n + f) . X is V19() real ext-real Element of REAL
n . X is V19() real ext-real Element of REAL
f . X is V19() real ext-real Element of REAL
(n . X) + (f . X) is V19() real ext-real Element of REAL
((proj (X,m)) . n) + (f . X) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
n is Element of the carrier of (REAL-NS m)
f is Element of the carrier of (REAL-NS m)
n - f is Element of the carrier of (REAL-NS m)
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (X,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
(Proj (X,m)) . (n - f) is Element of the carrier of (REAL-NS 1)
(Proj (X,m)) . n is Element of the carrier of (REAL-NS 1)
(Proj (X,m)) . f is Element of the carrier of (REAL-NS 1)
((Proj (X,m)) . n) - ((Proj (X,m)) . f) is Element of the carrier of (REAL-NS 1)
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
i . X is V19() real ext-real Element of REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
j . X is V19() real ext-real Element of REAL
proj (X,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (X,m)) . n is V19() real ext-real Element of REAL
<*((proj (X,m)) . n)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (X,m)) . n)] is set
{[1,((proj (X,m)) . n)]} is non empty V2() Function-like V55(1) set
(proj (X,m)) . f is V19() real ext-real Element of REAL
<*((proj (X,m)) . f)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (X,m)) . f)] is set
{[1,((proj (X,m)) . f)]} is non empty V2() Function-like V55(1) set
r is V19() real ext-real Element of REAL
<*r*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,r] is set
{[1,r]} is non empty V2() Function-like V55(1) set
s0 is V19() real ext-real Element of REAL
<*s0*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,s0] is set
{[1,s0]} is non empty V2() Function-like V55(1) set
(proj (X,m)) . (n - f) is V19() real ext-real Element of REAL
<*((proj (X,m)) . (n - f))*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (X,m)) . (n - f))] is set
{[1,((proj (X,m)) . (n - f))]} is non empty V2() Function-like V55(1) set
i - j is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
(proj (X,m)) . (i - j) is V19() real ext-real Element of REAL
<*((proj (X,m)) . (i - j))*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (X,m)) . (i - j))] is set
{[1,((proj (X,m)) . (i - j))]} is non empty V2() Function-like V55(1) set
(i - j) . X is V19() real ext-real Element of REAL
<*((i - j) . X)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((i - j) . X)] is set
{[1,((i - j) . X)]} is non empty V2() Function-like V55(1) set
(i . X) - (j . X) is V19() real ext-real Element of REAL
<*((i . X) - (j . X))*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((i . X) - (j . X))] is set
{[1,((i . X) - (j . X))]} is non empty V2() Function-like V55(1) set
<*r*> - <*s0*> is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
n - f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
proj (X,m) is Relation-like REAL m -defined REAL -valued Function-like V32( REAL m, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL m),REAL))
K11((REAL m),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL m),REAL)) is non finite set
(proj (X,m)) . (n - f) is V19() real ext-real Element of REAL
(proj (X,m)) . n is V19() real ext-real Element of REAL
(proj (X,m)) . f is V19() real ext-real Element of REAL
((proj (X,m)) . n) - ((proj (X,m)) . f) is V19() real ext-real Element of REAL
(n - f) . X is V19() real ext-real Element of REAL
n . X is V19() real ext-real Element of REAL
f . X is V19() real ext-real Element of REAL
(n . X) - (f . X) is V19() real ext-real Element of REAL
((proj (X,m)) . n) - (f . X) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
f is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
X is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
f - X is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (i,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
f * (Proj (i,n)) is Relation-like Function-like set
X * (Proj (i,n)) is Relation-like Function-like set
(f - X) * (Proj (i,n)) is Relation-like Function-like set
j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
r is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
j - r is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
dom (j - r) is set
dom ((f - X) * (Proj (i,n))) is set
dom j is set
dom r is set
s0 is Element of the carrier of (REAL-NS m)
(j - r) . s0 is Element of the carrier of (REAL-NS 1)
((f - X) * (Proj (i,n))) . s0 is set
rs0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(m) FinSequence-like FinSubsequence-like Element of REAL m
((f - X) * (Proj (i,n))) . rs0 is set
(f - X) . rs0 is set
(Proj (i,n)) . ((f - X) . rs0) is set
rs0 is Element of the carrier of (REAL-NS m)
f . rs0 is Element of the carrier of (REAL-NS n)
X . rs0 is Element of the carrier of (REAL-NS n)
(f . rs0) - (X . rs0) is Element of the carrier of (REAL-NS n)
(Proj (i,n)) . ((f . rs0) - (X . rs0)) is Element of the carrier of (REAL-NS 1)
(Proj (i,n)) . (f . rs0) is Element of the carrier of (REAL-NS 1)
(Proj (i,n)) . (X . rs0) is Element of the carrier of (REAL-NS 1)
((Proj (i,n)) . (f . rs0)) - ((Proj (i,n)) . (X . rs0)) is Element of the carrier of (REAL-NS 1)
j . rs0 is Element of the carrier of (REAL-NS 1)
(j . rs0) - ((Proj (i,n)) . (X . rs0)) is Element of the carrier of (REAL-NS 1)
r . rs0 is Element of the carrier of (REAL-NS 1)
(j . rs0) - (r . rs0) is Element of the carrier of (REAL-NS 1)
(j - r) . rs0 is set
s0 is set
(j - r) . s0 is set
((f - X) * (Proj (i,n))) . s0 is set
rs0 is Element of the carrier of (REAL-NS m)
(j - r) . rs0 is Element of the carrier of (REAL-NS 1)
((f - X) * (Proj (i,n))) . rs0 is set
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
f is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
||.f.|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) . f is V19() real ext-real Element of REAL
X is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (X,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
f * (Proj (X,n)) is Relation-like Function-like set
i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
||.i.|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . i is V19() real ext-real Element of REAL
BoundedLinearOperatorsNorm ((REAL-NS n),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL))
BoundedLinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS n),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1)))
K517( the carrier of (REAL-NS n),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS n),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS n),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS n),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS n),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS n),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS n),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS n),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))), LinearOperators ((REAL-NS n),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS n),(REAL-NS 1))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS n),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))), LinearOperators ((REAL-NS n),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS n),(REAL-NS 1)))),(LinearOperators ((REAL-NS n),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS n),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS n),(REAL-NS 1)),(LinearOperators ((REAL-NS n),(REAL-NS 1)))) #) is V107() 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 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS n),(REAL-NS 1)))) is set
K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS n),(REAL-NS 1))),REAL)) is non finite set
H1(n,1) . (Proj (X,n)) is V19() real ext-real Element of REAL
(H1(n,1) . (Proj (X,n))) * ||.f.|| is V19() real ext-real Element of REAL
1 * ||.f.|| is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
f is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
X is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
f - X is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
||.(f - X).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) . (f - X) is V19() real ext-real Element of REAL
i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
i - j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
||.(i - j).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . (i - j) is V19() real ext-real Element of REAL
r is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (r,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
f * (Proj (r,n)) is Relation-like Function-like set
X * (Proj (r,n)) is Relation-like Function-like set
(f - X) * (Proj (r,n)) is Relation-like Function-like set
m is V19() real ext-real Element of REAL
REAL 0 is non empty functional FinSequence-membered FinSequenceSet of REAL
0 -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
0 * m is V19() real ext-real Element of REAL
n is empty Relation-like NAT -defined REAL -valued V12() V13() V14() V16() V17() V18() V19() real ext-real non positive non negative Function-like one-to-one constant functional complex-yielding V37() V38() V39() finite V53() V55( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() bounded_below bounded_above real-bounded V76() Element of REAL 0
|.n.| is V19() real ext-real non negative Element of REAL
sqr n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr n) is V19() real ext-real Element of REAL
sqrt (Sum (sqr n)) is V19() real ext-real Element of REAL
0* 0 is empty Relation-like NAT -defined REAL -valued V12() V13() V14() V16() V17() V18() V19() real ext-real non positive non negative Function-like one-to-one constant functional complex-yielding V37() V38() V39() finite V53() V55( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() bounded_below bounded_above real-bounded V76() Element of REAL 0
0 |-> 0 is empty Relation-like empty-yielding NAT -defined REAL -valued V12() V13() V14() V16() V17() V18() V19() real ext-real non positive non negative Function-like one-to-one constant functional complex-yielding V37() V38() V39() finite V53() V55( 0 ) FinSequence-like FinSubsequence-like FinSequence-membered complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V66() bounded_below bounded_above real-bounded V76() Element of 0 -tuples_on REAL
n is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
n * m is V19() real ext-real Element of REAL
n + 1 is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL (n + 1) is non empty functional FinSequence-membered FinSequenceSet of REAL
(n + 1) -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
(n + 1) * m is V19() real ext-real Element of REAL
f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(n + 1) FinSequence-like FinSubsequence-like Element of REAL (n + 1)
|.f.| is V19() real ext-real non negative Element of REAL
sqr f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr f) is V19() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V19() real ext-real Element of REAL
f | n is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Seg n is finite V55(n) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
f | (Seg n) is Relation-like NAT -defined Function-like complex-yielding V37() V38() FinSubsequence-like set
len f is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
len (f | n) is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
f . j is V19() real ext-real Element of REAL
abs (f . j) is V19() real ext-real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(n) FinSequence-like FinSubsequence-like Element of REAL n
i . j is V19() real ext-real Element of REAL
abs (i . j) is V19() real ext-real Element of REAL
f . (n + 1) is V19() real ext-real Element of REAL
abs (f . (n + 1)) is V19() real ext-real Element of REAL
|.f.| ^2 is V19() real ext-real Element of REAL
K69(|.f.|,|.f.|) is V19() real ext-real non negative set
|.i.| is V19() real ext-real non negative Element of REAL
sqr i is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr i) is V19() real ext-real Element of REAL
sqrt (Sum (sqr i)) is V19() real ext-real Element of REAL
|.i.| ^2 is V19() real ext-real Element of REAL
K69(|.i.|,|.i.|) is V19() real ext-real non negative set
(f . (n + 1)) ^2 is V19() real ext-real Element of REAL
K69((f . (n + 1)),(f . (n + 1))) is V19() real ext-real set
(|.i.| ^2) + ((f . (n + 1)) ^2) is V19() real ext-real Element of REAL
(n * m) ^2 is V19() real ext-real Element of REAL
K69((n * m),(n * m)) is V19() real ext-real set
m ^2 is V19() real ext-real Element of REAL
K69(m,m) is V19() real ext-real set
((n * m) ^2) + (m ^2) is V19() real ext-real Element of REAL
2 * (n * m) is V19() real ext-real Element of REAL
(2 * (n * m)) * m is V19() real ext-real Element of REAL
(((n * m) ^2) + (m ^2)) + ((2 * (n * m)) * m) is V19() real ext-real Element of REAL
((n + 1) * m) ^2 is V19() real ext-real Element of REAL
K69(((n + 1) * m),((n + 1) * m)) is V19() real ext-real set
sqrt (((n + 1) * m) ^2) is V19() real ext-real Element of REAL
|.((n + 1) * m).| is V19() real ext-real Element of REAL
sqrt (|.f.| ^2) is V19() real ext-real Element of REAL
abs |.f.| is V19() real ext-real Element of REAL
abs (abs |.f.|) is V19() real ext-real Element of REAL
m is V19() real ext-real Element of REAL
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS n) is non empty V2() set
n * m is V19() real ext-real Element of REAL
f is Element of the carrier of (REAL-NS n)
||.f.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) is Relation-like the carrier of (REAL-NS n) -defined REAL -valued Function-like V32( the carrier of (REAL-NS n), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS n),REAL))
K11( the carrier of (REAL-NS n),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS n),REAL)) is non finite set
the U9 of (REAL-NS n) . f is V19() real ext-real Element of REAL
X is V12() V13() V14() V18() V19() real ext-real non negative finite V53() set
X + 1 is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
r is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
i + 1 is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
Proj (r,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (r,n)) . f is Element of the carrier of (REAL-NS 1)
||.((Proj (r,n)) . f).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . ((Proj (r,n)) . f) is V19() real ext-real Element of REAL
proj (r,n) is Relation-like REAL n -defined REAL -valued Function-like V32( REAL n, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL n),REAL))
K11((REAL n),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL n),REAL)) is non finite set
j is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(n) FinSequence-like FinSubsequence-like Element of REAL n
(proj (r,n)) . j is V19() real ext-real Element of REAL
<*((proj (r,n)) . j)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((proj (r,n)) . j)] is set
{[1,((proj (r,n)) . j)]} is non empty V2() Function-like V55(1) set
j . r is V19() real ext-real Element of REAL
<*(j . r)*> is non empty V2() Relation-like NAT -defined REAL -valued Function-like one-to-one constant complex-yielding V37() V38() V40() V41() V42() V43() finite V55(1) FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(j . r)] is set
{[1,(j . r)]} is non empty V2() Function-like V55(1) set
abs (j . r) is V19() real ext-real Element of REAL
|.j.| is V19() real ext-real non negative Element of REAL
sqr j is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr j) is V19() real ext-real Element of REAL
sqrt (Sum (sqr j)) is V19() real ext-real Element of REAL
m is V19() real ext-real Element of REAL
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
n * m is V19() real ext-real Element of REAL
f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite V55(n) FinSequence-like FinSubsequence-like Element of REAL n
|.f.| is V19() real ext-real non negative Element of REAL
sqr f is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
Sum (sqr f) is V19() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V19() real ext-real Element of REAL
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS n) is non empty V2() set
X is Element of the carrier of (REAL-NS n)
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (i,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (i,n)) . X is Element of the carrier of (REAL-NS 1)
||.((Proj (i,n)) . X).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . ((Proj (i,n)) . X) is V19() real ext-real Element of REAL
proj (i,n) is Relation-like REAL n -defined REAL -valued Function-like V32( REAL n, REAL ) complex-yielding V37() V38() Element of K10(K11((REAL n),REAL))
K11((REAL n),REAL) is complex-yielding V37() V38() non finite set
K10(K11((REAL n),REAL)) is non finite set
(proj (i,n)) . X is V19() real ext-real Element of REAL
|.((proj (i,n)) . X).| is V19() real ext-real Element of REAL
||.X.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) is Relation-like the carrier of (REAL-NS n) -defined REAL -valued Function-like V32( the carrier of (REAL-NS n), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS n),REAL))
K11( the carrier of (REAL-NS n),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS n),REAL)) is non finite set
the U9 of (REAL-NS n) . X is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
the carrier of H1(m,n) is non empty set
f is Relation-like Function-like Element of the carrier of H1(m,n)
||.f.|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) . f is V19() real ext-real Element of REAL
X is V19() real ext-real Element of REAL
n * X is V19() real ext-real Element of REAL
the carrier of H1(m,1) is non empty set
j is Element of the carrier of (REAL-NS m)
||.j.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . j is V19() real ext-real Element of REAL
r is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (r,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
f * (Proj (r,n)) is Relation-like Function-like set
rs0 is Relation-like Function-like Element of the carrier of H1(m,1)
rs0 is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) V149( REAL-NS m, REAL-NS 1) homogeneous Lipschitzian Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
rs0 . j is Element of the carrier of (REAL-NS 1)
||.(rs0 . j).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) is Relation-like the carrier of (REAL-NS 1) -defined REAL -valued Function-like V32( the carrier of (REAL-NS 1), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS 1),REAL))
K11( the carrier of (REAL-NS 1),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS 1),REAL)) is non finite set
the U9 of (REAL-NS 1) . (rs0 . j) is V19() real ext-real Element of REAL
||.rs0.|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . rs0 is V19() real ext-real Element of REAL
||.rs0.|| * ||.j.|| is V19() real ext-real Element of REAL
REAL m is non empty functional FinSequence-membered FinSequenceSet of REAL
m -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
dom (f * (Proj (r,n))) is set
f . j is Element of the carrier of (REAL-NS n)
(Proj (r,n)) . (f . j) is Element of the carrier of (REAL-NS 1)
X * ||.j.|| is V19() real ext-real Element of REAL
||.((Proj (r,n)) . (f . j)).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS 1) . ((Proj (r,n)) . (f . j)) is V19() real ext-real Element of REAL
||.(f . j).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) is Relation-like the carrier of (REAL-NS n) -defined REAL -valued Function-like V32( the carrier of (REAL-NS n), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS n),REAL))
K11( the carrier of (REAL-NS n),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS n),REAL)) is non finite set
the U9 of (REAL-NS n) . (f . j) is V19() real ext-real Element of REAL
n * (X * ||.j.||) is V19() real ext-real Element of REAL
Proj (1,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
f * (Proj (1,n)) is Relation-like Function-like set
r is Relation-like Function-like Element of the carrier of H1(m,1)
||.r.|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . r is V19() real ext-real Element of REAL
(n * X) * ||.j.|| is V19() real ext-real Element of REAL
(n * X) * 1 is V19() real ext-real Element of REAL
i is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) V149( REAL-NS m, REAL-NS n) homogeneous Lipschitzian Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
i . j is Element of the carrier of (REAL-NS n)
||.(i . j).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) . (i . j) is V19() real ext-real Element of REAL
modetrans (f,(REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) V149( REAL-NS m, REAL-NS n) homogeneous Lipschitzian Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
PreNorms (modetrans (f,(REAL-NS m),(REAL-NS n))) is non empty complex-membered ext-real-membered real-membered Element of K10(REAL)
{ ||.((modetrans (f,(REAL-NS m),(REAL-NS n))) . b1).|| where b1 is Element of the carrier of (REAL-NS m) : ||.b1.|| <= 1 } is set
r is ext-real set
s0 is Element of the carrier of (REAL-NS m)
(modetrans (f,(REAL-NS m),(REAL-NS n))) . s0 is Element of the carrier of (REAL-NS n)
||.((modetrans (f,(REAL-NS m),(REAL-NS n))) . s0).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) . ((modetrans (f,(REAL-NS m),(REAL-NS n))) . s0) is V19() real ext-real Element of REAL
||.s0.|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) . s0 is V19() real ext-real Element of REAL
i . s0 is Element of the carrier of (REAL-NS n)
||.(i . s0).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS n) . (i . s0) is V19() real ext-real Element of REAL
upper_bound (PreNorms (modetrans (f,(REAL-NS m),(REAL-NS n)))) is V19() real ext-real Element of REAL
(upper_bound (PreNorms (modetrans (f,(REAL-NS m),(REAL-NS n))))) - (n * X) is V19() real ext-real Element of REAL
(upper_bound (PreNorms (modetrans (f,(REAL-NS m),(REAL-NS n))))) - ((upper_bound (PreNorms (modetrans (f,(REAL-NS m),(REAL-NS n))))) - (n * X)) is V19() real ext-real Element of REAL
rs0 is V19() real ext-real set
PreNorms i is non empty complex-membered ext-real-membered real-membered Element of K10(REAL)
{ ||.(i . b1).|| where b1 is Element of the carrier of (REAL-NS m) : ||.b1.|| <= 1 } is set
upper_bound (PreNorms i) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
the carrier of (REAL-NS m) is non empty V2() set
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (REAL-NS n) is non empty V2() set
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
the carrier of H1(m,n) is non empty set
f is Relation-like Function-like Element of the carrier of H1(m,n)
X is Relation-like Function-like Element of the carrier of H1(m,n)
f - X is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
||.(f - X).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) . (f - X) is V19() real ext-real Element of REAL
i is V19() real ext-real Element of REAL
n * i is V19() real ext-real Element of REAL
the carrier of H1(m,1) is non empty set
r is Relation-like Function-like Element of the carrier of H1(m,1)
f - X is Relation-like Function-like Element of the carrier of H1(m,n)
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(f - X) * (Proj (j,n)) is Relation-like Function-like set
f * (Proj (j,n)) is Relation-like Function-like set
X * (Proj (j,n)) is Relation-like Function-like set
s0 is Relation-like Function-like Element of the carrier of H1(m,1)
rs0 is Relation-like Function-like Element of the carrier of H1(m,1)
s0 - rs0 is Relation-like Function-like Element of the carrier of H1(m,1)
||.r.|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . r is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS n) is non empty V2() set
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10( the carrier of (REAL-NS m)) is set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty Element of K10( 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 V107() V151() 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 K10( the carrier of K517( the carrier of (REAL-NS 1),(REAL-NS n)))
K517( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is non empty M4( 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 V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS 1),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K10(K11( 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 K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( 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 K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( 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 K517( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS 1),(REAL-NS n))) is set
K505(K517( 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))
K503(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11((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 V32(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))), LinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))), LinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS n))),K505(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) #) is V107() 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
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K505((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))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11((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 V32(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K504((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 V181() L16()
f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
X is Element of K10( the carrier of (REAL-NS m))
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
f `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), 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
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
dom f is Element of K10( the carrier of (REAL-NS m))
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (j,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
((Proj (j,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
dom (Proj (j,n)) is Element of K10( the carrier of (REAL-NS n))
K10( the carrier of (REAL-NS n)) is set
rng f is Element of K10( the carrier of (REAL-NS n))
dom ((Proj (j,n)) * f) is Element of K10( the carrier of (REAL-NS m))
r is Element of the carrier of (REAL-NS m)
reproj (i,r) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS m) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)))
K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)) is set
K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m))) is set
f * (reproj (i,r)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
Proj (i,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
(Proj (i,m)) . r is Element of the carrier of (REAL-NS 1)
(Proj (j,n)) * (f * (reproj (i,r))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
((Proj (j,n)) * f) * (reproj (i,r)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
dom (((Proj (j,n)) * f) `partial| (X,i)) is Element of K10( the carrier of (REAL-NS m))
r is Element of the carrier of (REAL-NS m)
(((Proj (j,n)) * f) `partial| (X,i)) /. r is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(f `partial| (X,i)) /. r is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
((f `partial| (X,i)) /. r) * (Proj (j,n)) is Relation-like Function-like set
reproj (i,r) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS m) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)))
f * (reproj (i,r)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(Proj (i,m)) . r is Element of the carrier of (REAL-NS 1)
partdiff (((Proj (j,n)) * f),r,i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
((Proj (j,n)) * f) * (reproj (i,r)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff ((((Proj (j,n)) * f) * (reproj (i,r))),((Proj (i,m)) . r)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(Proj (j,n)) * (f * (reproj (i,r))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff (((Proj (j,n)) * (f * (reproj (i,r)))),((Proj (i,m)) . r)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
diff ((f * (reproj (i,r))),((Proj (i,m)) . r)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(diff ((f * (reproj (i,r))),((Proj (i,m)) . r))) * (Proj (j,n)) is Relation-like Function-like set
partdiff (f,r,i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(partdiff (f,r,i)) * (Proj (j,n)) is Relation-like Function-like set
r is Element of the carrier of (REAL-NS m)
(((Proj (j,n)) * f) `partial| (X,i)) /. r is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
s0 is V19() real ext-real Element of REAL
(f `partial| (X,i)) /. r is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
rs0 is V19() real ext-real Element of REAL
rs0 is Element of the carrier of (REAL-NS m)
rs0 - r is Element of the carrier of (REAL-NS m)
||.(rs0 - r).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . (rs0 - r) is V19() real ext-real Element of REAL
(((Proj (j,n)) * f) `partial| (X,i)) /. rs0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
((((Proj (j,n)) * f) `partial| (X,i)) /. rs0) - ((((Proj (j,n)) * f) `partial| (X,i)) /. r) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
||.(((((Proj (j,n)) * f) `partial| (X,i)) /. rs0) - ((((Proj (j,n)) * f) `partial| (X,i)) /. r)).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) . (((((Proj (j,n)) * f) `partial| (X,i)) /. rs0) - ((((Proj (j,n)) * f) `partial| (X,i)) /. r)) is V19() real ext-real Element of REAL
(f `partial| (X,i)) /. rs0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
((f `partial| (X,i)) /. rs0) - ((f `partial| (X,i)) /. r) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
||.(((f `partial| (X,i)) /. rs0) - ((f `partial| (X,i)) /. r)).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) . (((f `partial| (X,i)) /. rs0) - ((f `partial| (X,i)) /. r)) is V19() real ext-real Element of REAL
((f `partial| (X,i)) /. r) * (Proj (j,n)) is Relation-like Function-like set
((f `partial| (X,i)) /. rs0) * (Proj (j,n)) is Relation-like Function-like set
s is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
i1 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
s - i1 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
||.(s - i1).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) . (s - i1) is V19() real ext-real Element of REAL
Proj (1,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (1,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
dom ((Proj (1,n)) * f) is Element of K10( the carrier of (REAL-NS m))
dom (Proj (1,n)) is Element of K10( the carrier of (REAL-NS n))
K10( the carrier of (REAL-NS n)) is set
rng f is Element of K10( the carrier of (REAL-NS n))
j is Element of the carrier of (REAL-NS m)
r is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (r,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (r,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
reproj (i,j) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS m) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)))
K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)) is set
K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m))) is set
((Proj (r,n)) * f) * (reproj (i,j)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
Proj (i,m) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
(Proj (i,m)) . j is Element of the carrier of (REAL-NS 1)
f * (reproj (i,j)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(Proj (r,n)) * (f * (reproj (i,j))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
dom (f `partial| (X,i)) is Element of K10( the carrier of (REAL-NS m))
j is Element of the carrier of (REAL-NS m)
(f `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
r is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (r,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
((f `partial| (X,i)) /. j) * (Proj (r,n)) is Relation-like Function-like set
(Proj (r,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (r,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
(((Proj (r,n)) * f) `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
reproj (i,j) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS m) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS m)))
f * (reproj (i,j)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
(Proj (i,m)) . j is Element of the carrier of (REAL-NS 1)
partdiff (f,j,i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(partdiff (f,j,i)) * (Proj (r,n)) is Relation-like Function-like set
diff ((f * (reproj (i,j))),((Proj (i,m)) . j)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
(diff ((f * (reproj (i,j))),((Proj (i,m)) . j))) * (Proj (r,n)) is Relation-like Function-like set
(Proj (r,n)) * (f * (reproj (i,j))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff (((Proj (r,n)) * (f * (reproj (i,j)))),((Proj (i,m)) . j)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
((Proj (r,n)) * f) * (reproj (i,j)) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS 1)))
diff ((((Proj (r,n)) * f) * (reproj (i,j))),((Proj (i,m)) . j)) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
partdiff (((Proj (r,n)) * f),j,i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
j is Element of the carrier of (REAL-NS m)
(f `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
r is V19() real ext-real Element of REAL
r / 2 is V19() real ext-real Element of REAL
(r / 2) / n is V19() real ext-real Element of REAL
Seg n is non empty finite V55(n) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
rs0 is V12() V13() V14() V18() V19() real ext-real non negative finite V53() set
rs0 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (rs0,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (rs0,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (rs0,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
(((Proj (rs0,n)) * f) `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
s is V19() real ext-real Element of REAL
rs0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
dom rs0 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
rng rs0 is complex-membered ext-real-membered real-membered Element of K10(REAL)
rs0 is non empty ext-real-membered set
s is non empty ext-real-membered left_end right_end set
min s is ext-real set
i1 is V19() real ext-real Element of REAL
x1 is set
rs0 . x1 is V19() real ext-real Element of REAL
p1 is V19() real ext-real Element of REAL
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (j,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (j,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
(((Proj (j,n)) * f) `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
j is Element of the carrier of (REAL-NS m)
j - j is Element of the carrier of (REAL-NS m)
||.(j - j).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . (j - j) is V19() real ext-real Element of REAL
(f `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
((f `partial| (X,i)) /. j) - ((f `partial| (X,i)) /. j) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))
||.(((f `partial| (X,i)) /. j) - ((f `partial| (X,i)) /. j)).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) . (((f `partial| (X,i)) /. j) - ((f `partial| (X,i)) /. j)) is V19() real ext-real Element of REAL
p0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
p1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (p1,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
((f `partial| (X,i)) /. j) * (Proj (p1,n)) is Relation-like Function-like set
jj is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
((f `partial| (X,i)) /. j) * (Proj (p1,n)) is Relation-like Function-like set
rs0 . p1 is V19() real ext-real Element of REAL
sj is V19() real ext-real Element of REAL
sj is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (sj,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (sj,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (sj,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
(((Proj (sj,n)) * f) `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(Proj (p1,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (p1,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
(((Proj (p1,n)) * f) `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
(((Proj (p1,n)) * f) `partial| (X,i)) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
p0 - jj is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))
||.(p0 - jj).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) . (p0 - jj) is V19() real ext-real Element of REAL
n * ((r / 2) / n) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS n) is non empty V2() set
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10( the carrier of (REAL-NS m)) is set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
X is Element of K10( the carrier of (REAL-NS m))
f `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
dom f is Element of K10( the carrier of (REAL-NS m))
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (i,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (i,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (i,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
dom (Proj (i,n)) is Element of K10( the carrier of (REAL-NS n))
K10( the carrier of (REAL-NS n)) is set
rng f is Element of K10( the carrier of (REAL-NS n))
dom ((Proj (i,n)) * f) is Element of K10( the carrier of (REAL-NS m))
j is Element of the carrier of (REAL-NS m)
dom (((Proj (i,n)) * f) `| X) is Element of K10( the carrier of (REAL-NS m))
j is Element of the carrier of (REAL-NS m)
(((Proj (i,n)) * f) `| X) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
(f `| X) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
((f `| X) /. j) * (Proj (i,n)) is Relation-like Function-like set
diff (((Proj (i,n)) * f),j) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
diff (f,j) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
(diff (f,j)) * (Proj (i,n)) is Relation-like Function-like set
j is Element of the carrier of (REAL-NS m)
(((Proj (i,n)) * f) `| X) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
r is V19() real ext-real Element of REAL
(f `| X) /. j is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
s0 is V19() real ext-real Element of REAL
rs0 is Element of the carrier of (REAL-NS m)
rs0 - j is Element of the carrier of (REAL-NS m)
||.(rs0 - j).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . (rs0 - j) is V19() real ext-real Element of REAL
(((Proj (i,n)) * f) `| X) /. rs0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
((((Proj (i,n)) * f) `| X) /. rs0) - ((((Proj (i,n)) * f) `| X) /. j) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
||.(((((Proj (i,n)) * f) `| X) /. rs0) - ((((Proj (i,n)) * f) `| X) /. j)).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . (((((Proj (i,n)) * f) `| X) /. rs0) - ((((Proj (i,n)) * f) `| X) /. j)) is V19() real ext-real Element of REAL
(f `| X) /. rs0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
((f `| X) /. rs0) - ((f `| X) /. j) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
||.(((f `| X) /. rs0) - ((f `| X) /. j)).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) . (((f `| X) /. rs0) - ((f `| X) /. j)) is V19() real ext-real Element of REAL
((f `| X) /. j) * (Proj (i,n)) is Relation-like Function-like set
((f `| X) /. rs0) * (Proj (i,n)) is Relation-like Function-like set
rs0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
s is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
rs0 - s is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
||.(rs0 - s).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . (rs0 - s) is V19() real ext-real Element of REAL
Proj (1,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (1,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
dom ((Proj (1,n)) * f) is Element of K10( the carrier of (REAL-NS m))
dom (Proj (1,n)) is Element of K10( the carrier of (REAL-NS n))
K10( the carrier of (REAL-NS n)) is set
rng f is Element of K10( the carrier of (REAL-NS n))
i is Element of the carrier of (REAL-NS m)
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (j,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
dom (f `| X) is Element of K10( the carrier of (REAL-NS m))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
i is Element of the carrier of (REAL-NS m)
(f `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
((f `| X) /. i) * (Proj (j,n)) is Relation-like Function-like set
(Proj (j,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (j,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
(((Proj (j,n)) * f) `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
diff (f,i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
(diff (f,i)) * (Proj (j,n)) is Relation-like Function-like set
diff (((Proj (j,n)) * f),i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
i is Element of the carrier of (REAL-NS m)
(f `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
j is V19() real ext-real Element of REAL
j / 2 is V19() real ext-real Element of REAL
(j / 2) / n is V19() real ext-real Element of REAL
Seg n is non empty finite V55(n) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of K10(NAT)
{ b1 where b1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT : ( 1 <= b1 & b1 <= n ) } is set
s0 is V12() V13() V14() V18() V19() real ext-real non negative finite V53() set
rs0 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (rs0,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (rs0,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (rs0,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
(((Proj (rs0,n)) * f) `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
rs0 is V19() real ext-real Element of REAL
s0 is Relation-like NAT -defined REAL -valued Function-like complex-yielding V37() V38() finite FinSequence-like FinSubsequence-like FinSequence of REAL
dom s0 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of K10(NAT)
rng s0 is complex-membered ext-real-membered real-membered Element of K10(REAL)
rs0 is non empty ext-real-membered set
rs0 is non empty ext-real-membered left_end right_end set
min rs0 is ext-real set
s is V19() real ext-real Element of REAL
i1 is set
s0 . i1 is V19() real ext-real Element of REAL
j is V19() real ext-real Element of REAL
x1 is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (x1,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (x1,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (x1,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
(((Proj (x1,n)) * f) `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
x1 is Element of the carrier of (REAL-NS m)
x1 - i is Element of the carrier of (REAL-NS m)
||.(x1 - i).|| is V19() real ext-real Element of REAL
the U9 of (REAL-NS m) is Relation-like the carrier of (REAL-NS m) -defined REAL -valued Function-like V32( the carrier of (REAL-NS m), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (REAL-NS m),REAL))
K11( the carrier of (REAL-NS m),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (REAL-NS m),REAL)) is non finite set
the U9 of (REAL-NS m) . (x1 - i) is V19() real ext-real Element of REAL
(f `| X) /. x1 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
((f `| X) /. x1) - ((f `| X) /. i) is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))
||.(((f `| X) /. x1) - ((f `| X) /. i)).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) . (((f `| X) /. x1) - ((f `| X) /. i)) is V19() real ext-real Element of REAL
p1 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
((f `| X) /. x1) * (Proj (j,n)) is Relation-like Function-like set
p0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
((f `| X) /. i) * (Proj (j,n)) is Relation-like Function-like set
s0 . j is V19() real ext-real Element of REAL
sj is V19() real ext-real Element of REAL
jj is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (jj,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (jj,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (jj,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
(((Proj (jj,n)) * f) `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
(Proj (j,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (j,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
(((Proj (j,n)) * f) `| X) /. i is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
(((Proj (j,n)) * f) `| X) /. x1 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
p1 - p0 is Relation-like Function-like Element of the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))
||.(p1 - p0).|| is V19() real ext-real Element of REAL
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is Relation-like the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -defined REAL -valued Function-like V32( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))), REAL ) complex-yielding V37() V38() Element of K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11( the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
the U9 of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) . (p1 - p0) is V19() real ext-real Element of REAL
n * ((j / 2) / n) is V19() real ext-real Element of REAL
m is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS m is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS m) is non empty V2() set
n is non empty V12() V13() V14() V18() V19() real ext-real positive non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of NAT
REAL-NS n is non empty V86() V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V181() V182() V192() L16()
the carrier of (REAL-NS n) is non empty V2() set
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10( the carrier of (REAL-NS m)) is set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) is non empty Element of K10( 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 V107() V151() 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 K10( the carrier of K517( the carrier of (REAL-NS 1),(REAL-NS n)))
K517( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is non empty M4( 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 V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))
K401((REAL-NS n)) is V88( REAL-NS n) Element of the carrier of (REAL-NS n)
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS 1),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS 1) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))
K11( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) is set
K10(K11( 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 K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( 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 K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS 1), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( 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 K517( the carrier of (REAL-NS 1),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS 1),(REAL-NS n))) is set
K505(K517( 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))
K503(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11((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 V32(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))), LinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS 1),(REAL-NS n))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined LinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))), LinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS 1),(REAL-NS n)))),(LinearOperators ((REAL-NS 1),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS 1),(REAL-NS n))),K505(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS 1),(REAL-NS n)),(LinearOperators ((REAL-NS 1),(REAL-NS n)))) #) is V107() 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
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K505((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))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11((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 V32(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS 1),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS 1),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))),K504((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 V181() L16()
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS n)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)))
K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))
K237( the carrier of (REAL-NS n), the carrier of (REAL-NS m),K401((REAL-NS n))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS n)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS n))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS n))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS n))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS n))
K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS n))),(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) -defined LinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))), LinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS n)))),(LinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS n))),K505(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS n)),(LinearOperators ((REAL-NS m),(REAL-NS n)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS n))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS n)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS n)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS n))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS n))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS n)))) is V181() L16()
f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS n) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS n)))
X is Element of K10( the carrier of (REAL-NS m))
f `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))) is non empty set
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS n))))) is set
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
f `partial| (X,j) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), 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
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))))) is set
Proj (i,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1))) is set
(Proj (i,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
((Proj (i,n)) * f) `partial| (X,j) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))))) is set
R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V179() V180() V182() V192() L16()
BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty Element of K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))))
R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
LinearOperators ((REAL-NS m),(REAL-NS 1)) is non empty functional Element of K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)))
K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty V107() V151() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) is non empty M4( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))
K237( the carrier of (REAL-NS 1), the carrier of (REAL-NS m),K401((REAL-NS 1))) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is set
K10(K11(K11(K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is set
FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1)) is Relation-like K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) -defined K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)) -valued Function-like V32(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) Element of K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))))
K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))) is non finite set
K10(K11(K11(REAL,K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1))),K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))) is non finite set
RLSStruct(# K165( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)),(FuncZero ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncAdd ( the carrier of (REAL-NS m),(REAL-NS 1))),(FuncExtMult ( the carrier of (REAL-NS m),(REAL-NS 1))) #) is strict RLSStruct
the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1)) is non empty set
K10( the carrier of K517( the carrier of (REAL-NS m),(REAL-NS 1))) is set
K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like Function-like Element of LinearOperators ((REAL-NS m),(REAL-NS 1))
K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((LinearOperators ((REAL-NS m),(REAL-NS 1))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined LinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))), LinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(LinearOperators ((REAL-NS m),(REAL-NS 1)))),(LinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
RLSStruct(# (LinearOperators ((REAL-NS m),(REAL-NS 1))),K505(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K503(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))),K504(K517( the carrier of (REAL-NS m),(REAL-NS 1)),(LinearOperators ((REAL-NS m),(REAL-NS 1)))) #) is V107() strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K10( the carrier of (R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Element of BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))
K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is Relation-like K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) -defined BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -valued Function-like V32(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))), BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) Element of K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is non finite set
K10(K11(K11(REAL,(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is non finite set
BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)) is Relation-like BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)) -defined REAL -valued Function-like V32( BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)), REAL ) complex-yielding V37() V38() Element of K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL))
K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL) is complex-yielding V37() V38() non finite set
K10(K11((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),REAL)) is non finite set
G16((BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))),K505((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K503((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),K504((R_VectorSpace_of_LinearOperators ((REAL-NS m),(REAL-NS 1))),(BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))),(BoundedLinearOperatorsNorm ((REAL-NS m),(REAL-NS 1)))) is V181() L16()
((Proj (i,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) is non empty set
K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))) is set
K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))))) is set
i is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
f `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS n)))))
j is V12() V13() V14() V18() V19() real ext-real non negative V24() V35() finite V53() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of NAT
Proj (j,n) is Relation-like the carrier of (REAL-NS n) -defined the carrier of (REAL-NS 1) -valued Function-like V32( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)) Element of K10(K11( the carrier of (REAL-NS n), the carrier of (REAL-NS 1)))
(Proj (j,n)) * f is Relation-like the carrier of (REAL-NS m) -defined the carrier of (REAL-NS 1) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (REAL-NS 1)))
((Proj (j,n)) * f) `| X is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS m),(REAL-NS 1)))))
((Proj (j,n)) * f) `partial| (X,i) is Relation-like the carrier of (REAL-NS m) -defined the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1))) -valued Function-like Element of K10(K11( the carrier of (REAL-NS m), the carrier of (R_NormSpace_of_BoundedLinearOperators ((REAL-NS 1),(REAL-NS 1)))))