:: CLOPBAN2 semantic presentation

REAL is non empty V46() V57() V58() V59() V63() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V57() V58() V59() V60() V61() V62() V63() Element of bool REAL
bool REAL is set
[:NAT,REAL:] is V35() V36() V37() set
bool [:NAT,REAL:] is set
COMPLEX is non empty V46() V57() V63() set
omega is non empty epsilon-transitive epsilon-connected ordinal V57() V58() V59() V60() V61() V62() V63() set
bool omega is set
bool NAT is set
RAT is non empty V46() V57() V58() V59() V60() V63() set
INT is non empty V46() V57() V58() V59() V60() V61() V63() set
[:NAT,COMPLEX:] is V35() set
bool [:NAT,COMPLEX:] is set
the_set_of_ComplexSequences is non empty set
[:the_set_of_ComplexSequences,the_set_of_ComplexSequences:] is set
[:[:the_set_of_ComplexSequences,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is set
bool [:[:the_set_of_ComplexSequences,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is set
[:COMPLEX,the_set_of_ComplexSequences:] is set
[:[:COMPLEX,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is set
bool [:[:COMPLEX,the_set_of_ComplexSequences:],the_set_of_ComplexSequences:] is set
Linear_Space_of_ComplexSequences is non empty strict CLSStruct
the carrier of Linear_Space_of_ComplexSequences is non empty set
bool the carrier of Linear_Space_of_ComplexSequences is set
the_set_of_l2ComplexSequences is Element of bool the carrier of Linear_Space_of_ComplexSequences
[:the_set_of_l2ComplexSequences,the_set_of_l2ComplexSequences:] is set
[:[:the_set_of_l2ComplexSequences,the_set_of_l2ComplexSequences:],COMPLEX:] is V35() set
bool [:[:the_set_of_l2ComplexSequences,the_set_of_l2ComplexSequences:],COMPLEX:] is set
the_set_of_l1ComplexSequences is non empty V144( Linear_Space_of_ComplexSequences ) Element of bool the carrier of Linear_Space_of_ComplexSequences
[:the_set_of_l1ComplexSequences,REAL:] is V35() V36() V37() set
bool [:the_set_of_l1ComplexSequences,REAL:] is set
[:COMPLEX,COMPLEX:] is V35() set
bool [:COMPLEX,COMPLEX:] is set
[:COMPLEX,REAL:] is V35() V36() V37() set
bool [:COMPLEX,REAL:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is V35() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is V35() V36() V37() set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is V35() V36() V37() set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is V17( RAT ) V35() V36() V37() set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is V17( RAT ) V35() V36() V37() set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is V17( RAT ) V17( INT ) V35() V36() V37() set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is V17( RAT ) V17( INT ) V35() V36() V37() set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is V17( RAT ) V17( INT ) V35() V36() V37() V38() set
[:[:NAT,NAT:],NAT:] is V17( RAT ) V17( INT ) V35() V36() V37() V38() set
bool [:[:NAT,NAT:],NAT:] is set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real Function-like functional ext-real non positive non negative V57() V58() V59() V60() V61() V62() V63() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real positive non negative V57() V58() V59() V60() V61() V62() Element of NAT
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real Function-like functional V30() V31() ext-real non positive non negative V57() V58() V59() V60() V61() V62() V63() Element of NAT
1r is complex Element of COMPLEX
- 1r is complex Element of COMPLEX
|.1r.| is complex real ext-real Element of REAL
Complex_l1_Space is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of Complex_l1_Space is non empty set
0. Complex_l1_Space is zero right_complementable Element of the carrier of Complex_l1_Space
the ZeroF of Complex_l1_Space is right_complementable Element of the carrier of Complex_l1_Space
CZeroseq is Element of the_set_of_ComplexSequences
[:NAT, the carrier of Complex_l1_Space:] is set
bool [:NAT, the carrier of Complex_l1_Space:] is set
0c is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real Function-like functional ext-real non positive non negative V57() V58() V59() V60() V61() V62() V63() Element of COMPLEX
c₁ is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of c₁ is non empty set
NRM is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of NRM is non empty set
[: the carrier of c₁, the carrier of NRM:] is set
bool [: the carrier of c₁, the carrier of NRM:] is set
UNIT is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of UNIT is non empty set
[: the carrier of NRM, the carrier of UNIT:] is set
bool [: the carrier of NRM, the carrier of UNIT:] is set
[: the carrier of c₁, the carrier of UNIT:] is set
bool [: the carrier of c₁, the carrier of UNIT:] is set
MULT is non empty V13() V16( the carrier of c₁) V17( the carrier of NRM) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of NRM) V171(c₁,NRM) V172(c₁,NRM) Element of bool [: the carrier of c₁, the carrier of NRM:]
ADD is non empty V13() V16( the carrier of NRM) V17( the carrier of UNIT) Function-like V23( the carrier of NRM) V27( the carrier of NRM, the carrier of UNIT) V171(NRM,UNIT) V172(NRM,UNIT) Element of bool [: the carrier of NRM, the carrier of UNIT:]
ADD * MULT is non empty V13() V16( the carrier of c₁) V17( the carrier of UNIT) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of UNIT) Element of bool [: the carrier of c₁, the carrier of UNIT:]
BS is right_complementable Element of the carrier of c₁
BLOP is complex set
BLOP * BS is right_complementable Element of the carrier of c₁
the Mult of c₁ is V13() V16([:COMPLEX, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([:COMPLEX, the carrier of c₁:]) V27([:COMPLEX, the carrier of c₁:], the carrier of c₁) Element of bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:]
[:COMPLEX, the carrier of c₁:] is set
[:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
K23(BLOP,BS) is set
the Mult of c₁ . K23(BLOP,BS) is set
(ADD * MULT) . (BLOP * BS) is right_complementable Element of the carrier of UNIT
MULT . (BLOP * BS) is right_complementable Element of the carrier of NRM
ADD . (MULT . (BLOP * BS)) is right_complementable Element of the carrier of UNIT
MULT . BS is right_complementable Element of the carrier of NRM
BLOP * (MULT . BS) is right_complementable Element of the carrier of NRM
the Mult of NRM is V13() V16([:COMPLEX, the carrier of NRM:]) V17( the carrier of NRM) Function-like V23([:COMPLEX, the carrier of NRM:]) V27([:COMPLEX, the carrier of NRM:], the carrier of NRM) Element of bool [:[:COMPLEX, the carrier of NRM:], the carrier of NRM:]
[:COMPLEX, the carrier of NRM:] is set
[:[:COMPLEX, the carrier of NRM:], the carrier of NRM:] is set
bool [:[:COMPLEX, the carrier of NRM:], the carrier of NRM:] is set
K23(BLOP,(MULT . BS)) is set
the Mult of NRM . K23(BLOP,(MULT . BS)) is set
ADD . (BLOP * (MULT . BS)) is right_complementable Element of the carrier of UNIT
ADD . (MULT . BS) is right_complementable Element of the carrier of UNIT
BLOP * (ADD . (MULT . BS)) is right_complementable Element of the carrier of UNIT
the Mult of UNIT is V13() V16([:COMPLEX, the carrier of UNIT:]) V17( the carrier of UNIT) Function-like V23([:COMPLEX, the carrier of UNIT:]) V27([:COMPLEX, the carrier of UNIT:], the carrier of UNIT) Element of bool [:[:COMPLEX, the carrier of UNIT:], the carrier of UNIT:]
[:COMPLEX, the carrier of UNIT:] is set
[:[:COMPLEX, the carrier of UNIT:], the carrier of UNIT:] is set
bool [:[:COMPLEX, the carrier of UNIT:], the carrier of UNIT:] is set
K23(BLOP,(ADD . (MULT . BS))) is set
the Mult of UNIT . K23(BLOP,(ADD . (MULT . BS))) is set
(ADD * MULT) . BS is right_complementable Element of the carrier of UNIT
BLOP * ((ADD * MULT) . BS) is right_complementable Element of the carrier of UNIT
K23(BLOP,((ADD * MULT) . BS)) is set
the Mult of UNIT . K23(BLOP,((ADD * MULT) . BS)) is set
BS is right_complementable Element of the carrier of c₁
BLOP is right_complementable Element of the carrier of c₁
BS + BLOP is right_complementable Element of the carrier of c₁
the addF of c₁ is V13() V16([: the carrier of c₁, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([: the carrier of c₁, the carrier of c₁:]) V27([: the carrier of c₁, the carrier of c₁:], the carrier of c₁) Element of bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
[:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
the addF of c₁ . (BS,BLOP) is right_complementable Element of the carrier of c₁
K23(BS,BLOP) is set
the addF of c₁ . K23(BS,BLOP) is set
(ADD * MULT) . (BS + BLOP) is right_complementable Element of the carrier of UNIT
MULT . (BS + BLOP) is right_complementable Element of the carrier of NRM
ADD . (MULT . (BS + BLOP)) is right_complementable Element of the carrier of UNIT
MULT . BS is right_complementable Element of the carrier of NRM
MULT . BLOP is right_complementable Element of the carrier of NRM
(MULT . BS) + (MULT . BLOP) is right_complementable Element of the carrier of NRM
the addF of NRM is V13() V16([: the carrier of NRM, the carrier of NRM:]) V17( the carrier of NRM) Function-like V23([: the carrier of NRM, the carrier of NRM:]) V27([: the carrier of NRM, the carrier of NRM:], the carrier of NRM) Element of bool [:[: the carrier of NRM, the carrier of NRM:], the carrier of NRM:]
[: the carrier of NRM, the carrier of NRM:] is set
[:[: the carrier of NRM, the carrier of NRM:], the carrier of NRM:] is set
bool [:[: the carrier of NRM, the carrier of NRM:], the carrier of NRM:] is set
the addF of NRM . ((MULT . BS),(MULT . BLOP)) is right_complementable Element of the carrier of NRM
K23((MULT . BS),(MULT . BLOP)) is set
the addF of NRM . K23((MULT . BS),(MULT . BLOP)) is set
ADD . ((MULT . BS) + (MULT . BLOP)) is right_complementable Element of the carrier of UNIT
ADD . (MULT . BS) is right_complementable Element of the carrier of UNIT
ADD . (MULT . BLOP) is right_complementable Element of the carrier of UNIT
(ADD . (MULT . BS)) + (ADD . (MULT . BLOP)) is right_complementable Element of the carrier of UNIT
the addF of UNIT is V13() V16([: the carrier of UNIT, the carrier of UNIT:]) V17( the carrier of UNIT) Function-like V23([: the carrier of UNIT, the carrier of UNIT:]) V27([: the carrier of UNIT, the carrier of UNIT:], the carrier of UNIT) Element of bool [:[: the carrier of UNIT, the carrier of UNIT:], the carrier of UNIT:]
[: the carrier of UNIT, the carrier of UNIT:] is set
[:[: the carrier of UNIT, the carrier of UNIT:], the carrier of UNIT:] is set
bool [:[: the carrier of UNIT, the carrier of UNIT:], the carrier of UNIT:] is set
the addF of UNIT . ((ADD . (MULT . BS)),(ADD . (MULT . BLOP))) is right_complementable Element of the carrier of UNIT
K23((ADD . (MULT . BS)),(ADD . (MULT . BLOP))) is set
the addF of UNIT . K23((ADD . (MULT . BS)),(ADD . (MULT . BLOP))) is set
(ADD * MULT) . BS is right_complementable Element of the carrier of UNIT
((ADD * MULT) . BS) + (ADD . (MULT . BLOP)) is right_complementable Element of the carrier of UNIT
the addF of UNIT . (((ADD * MULT) . BS),(ADD . (MULT . BLOP))) is right_complementable Element of the carrier of UNIT
K23(((ADD * MULT) . BS),(ADD . (MULT . BLOP))) is set
the addF of UNIT . K23(((ADD * MULT) . BS),(ADD . (MULT . BLOP))) is set
(ADD * MULT) . BLOP is right_complementable Element of the carrier of UNIT
((ADD * MULT) . BS) + ((ADD * MULT) . BLOP) is right_complementable Element of the carrier of UNIT
the addF of UNIT . (((ADD * MULT) . BS),((ADD * MULT) . BLOP)) is right_complementable Element of the carrier of UNIT
K23(((ADD * MULT) . BS),((ADD * MULT) . BLOP)) is set
the addF of UNIT . K23(((ADD * MULT) . BS),((ADD * MULT) . BLOP)) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
NRM is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of NRM is non empty set
[: the carrier of c₁, the carrier of NRM:] is set
bool [: the carrier of c₁, the carrier of NRM:] is set
UNIT is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of UNIT is non empty set
[: the carrier of NRM, the carrier of UNIT:] is set
bool [: the carrier of NRM, the carrier of UNIT:] is set
[: the carrier of c₁, the carrier of UNIT:] is set
bool [: the carrier of c₁, the carrier of UNIT:] is set
BoundedLinearOperatorsNorm (NRM,UNIT) is non empty V13() V16( BoundedLinearOperators (NRM,UNIT)) V17( REAL ) Function-like V23( BoundedLinearOperators (NRM,UNIT)) V27( BoundedLinearOperators (NRM,UNIT), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (NRM,UNIT)),REAL:]
BoundedLinearOperators (NRM,UNIT) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (NRM,UNIT))
C_VectorSpace_of_LinearOperators (NRM,UNIT) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (NRM,UNIT) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of NRM,UNIT))
ComplexVectSpace ( the carrier of NRM,UNIT) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of NRM,UNIT)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of NRM,UNIT)) is set
Zero_ ((LinearOperators (NRM,UNIT)),(ComplexVectSpace ( the carrier of NRM,UNIT))) is V13() Function-like Element of LinearOperators (NRM,UNIT)
Add_ ((LinearOperators (NRM,UNIT)),(ComplexVectSpace ( the carrier of NRM,UNIT))) is V13() V16([:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):]) V17( LinearOperators (NRM,UNIT)) Function-like V23([:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):]) V27([:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):], LinearOperators (NRM,UNIT)) Element of bool [:[:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):],(LinearOperators (NRM,UNIT)):]
[:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):] is set
[:[:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):],(LinearOperators (NRM,UNIT)):] is set
bool [:[:(LinearOperators (NRM,UNIT)),(LinearOperators (NRM,UNIT)):],(LinearOperators (NRM,UNIT)):] is set
Mult_ ((LinearOperators (NRM,UNIT)),(ComplexVectSpace ( the carrier of NRM,UNIT))) is V13() V16([:COMPLEX,(LinearOperators (NRM,UNIT)):]) V17( LinearOperators (NRM,UNIT)) Function-like V23([:COMPLEX,(LinearOperators (NRM,UNIT)):]) V27([:COMPLEX,(LinearOperators (NRM,UNIT)):], LinearOperators (NRM,UNIT)) Element of bool [:[:COMPLEX,(LinearOperators (NRM,UNIT)):],(LinearOperators (NRM,UNIT)):]
[:COMPLEX,(LinearOperators (NRM,UNIT)):] is set
[:[:COMPLEX,(LinearOperators (NRM,UNIT)):],(LinearOperators (NRM,UNIT)):] is set
bool [:[:COMPLEX,(LinearOperators (NRM,UNIT)):],(LinearOperators (NRM,UNIT)):] is set
CLSStruct(# (LinearOperators (NRM,UNIT)),(Zero_ ((LinearOperators (NRM,UNIT)),(ComplexVectSpace ( the carrier of NRM,UNIT)))),(Add_ ((LinearOperators (NRM,UNIT)),(ComplexVectSpace ( the carrier of NRM,UNIT)))),(Mult_ ((LinearOperators (NRM,UNIT)),(ComplexVectSpace ( the carrier of NRM,UNIT)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (NRM,UNIT)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (NRM,UNIT)) is set
[:(BoundedLinearOperators (NRM,UNIT)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (NRM,UNIT)),REAL:] is set
BoundedLinearOperatorsNorm (c₁,NRM) is non empty V13() V16( BoundedLinearOperators (c₁,NRM)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,NRM)) V27( BoundedLinearOperators (c₁,NRM), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,NRM)),REAL:]
BoundedLinearOperators (c₁,NRM) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,NRM))
C_VectorSpace_of_LinearOperators (c₁,NRM) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,NRM) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,NRM))
ComplexVectSpace ( the carrier of c₁,NRM) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,NRM)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,NRM)) is set
Zero_ ((LinearOperators (c₁,NRM)),(ComplexVectSpace ( the carrier of c₁,NRM))) is V13() Function-like Element of LinearOperators (c₁,NRM)
Add_ ((LinearOperators (c₁,NRM)),(ComplexVectSpace ( the carrier of c₁,NRM))) is V13() V16([:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):]) V17( LinearOperators (c₁,NRM)) Function-like V23([:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):]) V27([:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):], LinearOperators (c₁,NRM)) Element of bool [:[:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):],(LinearOperators (c₁,NRM)):]
[:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):] is set
[:[:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):],(LinearOperators (c₁,NRM)):] is set
bool [:[:(LinearOperators (c₁,NRM)),(LinearOperators (c₁,NRM)):],(LinearOperators (c₁,NRM)):] is set
Mult_ ((LinearOperators (c₁,NRM)),(ComplexVectSpace ( the carrier of c₁,NRM))) is V13() V16([:COMPLEX,(LinearOperators (c₁,NRM)):]) V17( LinearOperators (c₁,NRM)) Function-like V23([:COMPLEX,(LinearOperators (c₁,NRM)):]) V27([:COMPLEX,(LinearOperators (c₁,NRM)):], LinearOperators (c₁,NRM)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,NRM)):],(LinearOperators (c₁,NRM)):]
[:COMPLEX,(LinearOperators (c₁,NRM)):] is set
[:[:COMPLEX,(LinearOperators (c₁,NRM)):],(LinearOperators (c₁,NRM)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,NRM)):],(LinearOperators (c₁,NRM)):] is set
CLSStruct(# (LinearOperators (c₁,NRM)),(Zero_ ((LinearOperators (c₁,NRM)),(ComplexVectSpace ( the carrier of c₁,NRM)))),(Add_ ((LinearOperators (c₁,NRM)),(ComplexVectSpace ( the carrier of c₁,NRM)))),(Mult_ ((LinearOperators (c₁,NRM)),(ComplexVectSpace ( the carrier of c₁,NRM)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,NRM)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,NRM)) is set
[:(BoundedLinearOperators (c₁,NRM)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,NRM)),REAL:] is set
BoundedLinearOperatorsNorm (c₁,UNIT) is non empty V13() V16( BoundedLinearOperators (c₁,UNIT)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,UNIT)) V27( BoundedLinearOperators (c₁,UNIT), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,UNIT)),REAL:]
BoundedLinearOperators (c₁,UNIT) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,UNIT))
C_VectorSpace_of_LinearOperators (c₁,UNIT) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,UNIT) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,UNIT))
ComplexVectSpace ( the carrier of c₁,UNIT) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,UNIT)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,UNIT)) is set
Zero_ ((LinearOperators (c₁,UNIT)),(ComplexVectSpace ( the carrier of c₁,UNIT))) is V13() Function-like Element of LinearOperators (c₁,UNIT)
Add_ ((LinearOperators (c₁,UNIT)),(ComplexVectSpace ( the carrier of c₁,UNIT))) is V13() V16([:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):]) V17( LinearOperators (c₁,UNIT)) Function-like V23([:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):]) V27([:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):], LinearOperators (c₁,UNIT)) Element of bool [:[:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):],(LinearOperators (c₁,UNIT)):]
[:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):] is set
[:[:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):],(LinearOperators (c₁,UNIT)):] is set
bool [:[:(LinearOperators (c₁,UNIT)),(LinearOperators (c₁,UNIT)):],(LinearOperators (c₁,UNIT)):] is set
Mult_ ((LinearOperators (c₁,UNIT)),(ComplexVectSpace ( the carrier of c₁,UNIT))) is V13() V16([:COMPLEX,(LinearOperators (c₁,UNIT)):]) V17( LinearOperators (c₁,UNIT)) Function-like V23([:COMPLEX,(LinearOperators (c₁,UNIT)):]) V27([:COMPLEX,(LinearOperators (c₁,UNIT)):], LinearOperators (c₁,UNIT)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,UNIT)):],(LinearOperators (c₁,UNIT)):]
[:COMPLEX,(LinearOperators (c₁,UNIT)):] is set
[:[:COMPLEX,(LinearOperators (c₁,UNIT)):],(LinearOperators (c₁,UNIT)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,UNIT)):],(LinearOperators (c₁,UNIT)):] is set
CLSStruct(# (LinearOperators (c₁,UNIT)),(Zero_ ((LinearOperators (c₁,UNIT)),(ComplexVectSpace ( the carrier of c₁,UNIT)))),(Add_ ((LinearOperators (c₁,UNIT)),(ComplexVectSpace ( the carrier of c₁,UNIT)))),(Mult_ ((LinearOperators (c₁,UNIT)),(ComplexVectSpace ( the carrier of c₁,UNIT)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,UNIT)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,UNIT)) is set
[:(BoundedLinearOperators (c₁,UNIT)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,UNIT)),REAL:] is set
MULT is non empty V13() V16( the carrier of c₁) V17( the carrier of NRM) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of NRM) V171(c₁,NRM) V172(c₁,NRM) Lipschitzian Element of bool [: the carrier of c₁, the carrier of NRM:]
(BoundedLinearOperatorsNorm (c₁,NRM)) . MULT is complex real ext-real set
ADD is non empty V13() V16( the carrier of NRM) V17( the carrier of UNIT) Function-like V23( the carrier of NRM) V27( the carrier of NRM, the carrier of UNIT) V171(NRM,UNIT) V172(NRM,UNIT) Lipschitzian Element of bool [: the carrier of NRM, the carrier of UNIT:]
ADD * MULT is non empty V13() V16( the carrier of c₁) V17( the carrier of UNIT) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of UNIT) Element of bool [: the carrier of c₁, the carrier of UNIT:]
(BoundedLinearOperatorsNorm (NRM,UNIT)) . ADD is complex real ext-real set
((BoundedLinearOperatorsNorm (NRM,UNIT)) . ADD) * ((BoundedLinearOperatorsNorm (c₁,NRM)) . MULT) is complex real ext-real set
(BoundedLinearOperatorsNorm (c₁,UNIT)) . (ADD * MULT) is complex real ext-real set
C_NormSpace_of_BoundedLinearOperators (c₁,NRM) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
Zero_ ((BoundedLinearOperators (c₁,NRM)),(C_VectorSpace_of_LinearOperators (c₁,NRM))) is Element of BoundedLinearOperators (c₁,NRM)
Add_ ((BoundedLinearOperators (c₁,NRM)),(C_VectorSpace_of_LinearOperators (c₁,NRM))) is V13() V16([:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):]) V17( BoundedLinearOperators (c₁,NRM)) Function-like V23([:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):]) V27([:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):], BoundedLinearOperators (c₁,NRM)) Element of bool [:[:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):],(BoundedLinearOperators (c₁,NRM)):]
[:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):] is set
[:[:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):],(BoundedLinearOperators (c₁,NRM)):] is set
bool [:[:(BoundedLinearOperators (c₁,NRM)),(BoundedLinearOperators (c₁,NRM)):],(BoundedLinearOperators (c₁,NRM)):] is set
Mult_ ((BoundedLinearOperators (c₁,NRM)),(C_VectorSpace_of_LinearOperators (c₁,NRM))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,NRM)):]) V17( BoundedLinearOperators (c₁,NRM)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,NRM)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,NRM)):], BoundedLinearOperators (c₁,NRM)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,NRM)):],(BoundedLinearOperators (c₁,NRM)):]
[:COMPLEX,(BoundedLinearOperators (c₁,NRM)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,NRM)):],(BoundedLinearOperators (c₁,NRM)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,NRM)):],(BoundedLinearOperators (c₁,NRM)):] is set
CNORMSTR(# (BoundedLinearOperators (c₁,NRM)),(Zero_ ((BoundedLinearOperators (c₁,NRM)),(C_VectorSpace_of_LinearOperators (c₁,NRM)))),(Add_ ((BoundedLinearOperators (c₁,NRM)),(C_VectorSpace_of_LinearOperators (c₁,NRM)))),(Mult_ ((BoundedLinearOperators (c₁,NRM)),(C_VectorSpace_of_LinearOperators (c₁,NRM)))),(BoundedLinearOperatorsNorm (c₁,NRM)) #) is non empty strict CNORMSTR
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)) is non empty set
C_NormSpace_of_BoundedLinearOperators (NRM,UNIT) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
Zero_ ((BoundedLinearOperators (NRM,UNIT)),(C_VectorSpace_of_LinearOperators (NRM,UNIT))) is Element of BoundedLinearOperators (NRM,UNIT)
Add_ ((BoundedLinearOperators (NRM,UNIT)),(C_VectorSpace_of_LinearOperators (NRM,UNIT))) is V13() V16([:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):]) V17( BoundedLinearOperators (NRM,UNIT)) Function-like V23([:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):]) V27([:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):], BoundedLinearOperators (NRM,UNIT)) Element of bool [:[:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):],(BoundedLinearOperators (NRM,UNIT)):]
[:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):] is set
[:[:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):],(BoundedLinearOperators (NRM,UNIT)):] is set
bool [:[:(BoundedLinearOperators (NRM,UNIT)),(BoundedLinearOperators (NRM,UNIT)):],(BoundedLinearOperators (NRM,UNIT)):] is set
Mult_ ((BoundedLinearOperators (NRM,UNIT)),(C_VectorSpace_of_LinearOperators (NRM,UNIT))) is V13() V16([:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):]) V17( BoundedLinearOperators (NRM,UNIT)) Function-like V23([:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):]) V27([:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):], BoundedLinearOperators (NRM,UNIT)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):],(BoundedLinearOperators (NRM,UNIT)):]
[:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):] is set
[:[:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):],(BoundedLinearOperators (NRM,UNIT)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (NRM,UNIT)):],(BoundedLinearOperators (NRM,UNIT)):] is set
CNORMSTR(# (BoundedLinearOperators (NRM,UNIT)),(Zero_ ((BoundedLinearOperators (NRM,UNIT)),(C_VectorSpace_of_LinearOperators (NRM,UNIT)))),(Add_ ((BoundedLinearOperators (NRM,UNIT)),(C_VectorSpace_of_LinearOperators (NRM,UNIT)))),(Mult_ ((BoundedLinearOperators (NRM,UNIT)),(C_VectorSpace_of_LinearOperators (NRM,UNIT)))),(BoundedLinearOperatorsNorm (NRM,UNIT)) #) is non empty strict CNORMSTR
the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)) is non empty set
BLOP is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT))
||.BLOP.|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)) is non empty V13() V16( the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT))) V17( REAL ) Function-like V23( the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT))) V27( the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)), REAL ) V35() V36() V37() Element of bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)),REAL:]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)),REAL:] is V35() V36() V37() set
bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)),REAL:] is set
the normF of (C_NormSpace_of_BoundedLinearOperators (NRM,UNIT)) . BLOP is complex real ext-real Element of REAL
RBLOP is right_complementable Element of the carrier of c₁
MULT . RBLOP is right_complementable Element of the carrier of NRM
||.(MULT . RBLOP).|| is complex real ext-real Element of REAL
the normF of NRM is non empty V13() V16( the carrier of NRM) V17( REAL ) Function-like V23( the carrier of NRM) V27( the carrier of NRM, REAL ) V35() V36() V37() Element of bool [: the carrier of NRM,REAL:]
[: the carrier of NRM,REAL:] is V35() V36() V37() set
bool [: the carrier of NRM,REAL:] is set
the normF of NRM . (MULT . RBLOP) is complex real ext-real Element of REAL
||.BLOP.|| * ||.(MULT . RBLOP).|| is complex real ext-real Element of REAL
BS is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM))
||.BS.|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)) is non empty V13() V16( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM))) V17( REAL ) Function-like V23( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM))) V27( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)), REAL ) V35() V36() V37() Element of bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)),REAL:]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)),REAL:] is V35() V36() V37() set
bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)),REAL:] is set
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,NRM)) . BS is complex real ext-real Element of REAL
||.RBLOP.|| is complex real ext-real Element of REAL
the normF of c₁ is non empty V13() V16( the carrier of c₁) V17( REAL ) Function-like V23( the carrier of c₁) V27( the carrier of c₁, REAL ) V35() V36() V37() Element of bool [: the carrier of c₁,REAL:]
[: the carrier of c₁,REAL:] is V35() V36() V37() set
bool [: the carrier of c₁,REAL:] is set
the normF of c₁ . RBLOP is complex real ext-real Element of REAL
||.BS.|| * ||.RBLOP.|| is complex real ext-real Element of REAL
||.BLOP.|| * (||.BS.|| * ||.RBLOP.||) is complex real ext-real Element of REAL
(ADD * MULT) . RBLOP is right_complementable Element of the carrier of UNIT
||.((ADD * MULT) . RBLOP).|| is complex real ext-real Element of REAL
the normF of UNIT is non empty V13() V16( the carrier of UNIT) V17( REAL ) Function-like V23( the carrier of UNIT) V27( the carrier of UNIT, REAL ) V35() V36() V37() Element of bool [: the carrier of UNIT,REAL:]
[: the carrier of UNIT,REAL:] is V35() V36() V37() set
bool [: the carrier of UNIT,REAL:] is set
the normF of UNIT . ((ADD * MULT) . RBLOP) is complex real ext-real Element of REAL
ADD . (MULT . RBLOP) is right_complementable Element of the carrier of UNIT
||.(ADD . (MULT . RBLOP)).|| is complex real ext-real Element of REAL
the normF of UNIT . (ADD . (MULT . RBLOP)) is complex real ext-real Element of REAL
||.BLOP.|| * ||.BS.|| is complex real ext-real Element of REAL
(||.BLOP.|| * ||.BS.||) * ||.RBLOP.|| is complex real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of c₁
||.seq1.|| is complex real ext-real Element of REAL
the normF of c₁ . seq1 is complex real ext-real Element of REAL
(||.BLOP.|| * ||.BS.||) * ||.seq1.|| is complex real ext-real Element of REAL
(||.BLOP.|| * ||.BS.||) * 1 is complex real ext-real Element of REAL
(ADD * MULT) . seq1 is right_complementable Element of the carrier of UNIT
||.((ADD * MULT) . seq1).|| is complex real ext-real Element of REAL
the normF of UNIT . ((ADD * MULT) . seq1) is complex real ext-real Element of REAL
seq1 is complex real ext-real Element of REAL
seq is non empty V13() V16( the carrier of c₁) V17( the carrier of UNIT) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of UNIT) V171(c₁,UNIT) V172(c₁,UNIT) Lipschitzian Element of bool [: the carrier of c₁, the carrier of UNIT:]
PreNorms seq is non empty V57() V58() V59() Element of bool REAL
{ ||.(seq . b₁).|| where b₁ is right_complementable Element of the carrier of c₁ : ||.b₁.|| <= 1 } is set
g1 is right_complementable Element of the carrier of c₁
seq . g1 is right_complementable Element of the carrier of UNIT
||.(seq . g1).|| is complex real ext-real Element of REAL
the normF of UNIT . (seq . g1) is complex real ext-real Element of REAL
||.g1.|| is complex real ext-real Element of REAL
the normF of c₁ . g1 is complex real ext-real Element of REAL
upper_bound (PreNorms seq) is complex real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of c₁
(ADD * MULT) . seq1 is right_complementable Element of the carrier of UNIT
||.((ADD * MULT) . seq1).|| is complex real ext-real Element of REAL
the normF of UNIT . ((ADD * MULT) . seq1) is complex real ext-real Element of REAL
||.seq1.|| is complex real ext-real Element of REAL
the normF of c₁ . seq1 is complex real ext-real Element of REAL
(((BoundedLinearOperatorsNorm (NRM,UNIT)) . ADD) * ((BoundedLinearOperatorsNorm (c₁,NRM)) . MULT)) * ||.seq1.|| is complex real ext-real Element of REAL
g1 is complex real ext-real set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
NRM is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT * NRM is V13() Function-like set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
NRM is Element of BoundedLinearOperators (c₁,c₁)
UNIT is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (NRM,UNIT) is Element of BoundedLinearOperators (c₁,c₁)
K23(NRM,UNIT) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(NRM,UNIT) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
NRM is Element of BoundedLinearOperators (c₁,c₁)
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
UNIT is Element of BoundedLinearOperators (c₁,c₁)
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
UNIT is complex set
NRM is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (UNIT,NRM) is set
K23(UNIT,NRM) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(UNIT,NRM) is set
MULT is complex Element of COMPLEX
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (MULT,NRM) is Element of BoundedLinearOperators (c₁,c₁)
K23(MULT,NRM) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(MULT,NRM) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
NRM is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
UNIT is Element of BoundedLinearOperators (c₁,c₁)
MULT is Element of BoundedLinearOperators (c₁,c₁)
NRM . (UNIT,MULT) is Element of BoundedLinearOperators (c₁,c₁)
K23(UNIT,MULT) is set
NRM . K23(UNIT,MULT) is set
(c₁,MULT,UNIT) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (MULT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
NRM is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
UNIT is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
MULT is Element of BoundedLinearOperators (c₁,c₁)
ADD is Element of BoundedLinearOperators (c₁,c₁)
NRM . (MULT,ADD) is Element of BoundedLinearOperators (c₁,c₁)
K23(MULT,ADD) is set
NRM . K23(MULT,ADD) is set
(c₁,ADD,MULT) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (ADD,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans (MULT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (ADD,c₁,c₁)),(modetrans (MULT,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT . (MULT,ADD) is Element of BoundedLinearOperators (c₁,c₁)
UNIT . K23(MULT,ADD) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
NRM is right_complementable Element of the carrier of c₁
UNIT is right_complementable Element of the carrier of c₁
NRM + UNIT is right_complementable Element of the carrier of c₁
the addF of c₁ is V13() V16([: the carrier of c₁, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([: the carrier of c₁, the carrier of c₁:]) V27([: the carrier of c₁, the carrier of c₁:], the carrier of c₁) Element of bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:]
[:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
the addF of c₁ . (NRM,UNIT) is right_complementable Element of the carrier of c₁
K23(NRM,UNIT) is set
the addF of c₁ . K23(NRM,UNIT) is set
(id the carrier of c₁) . (NRM + UNIT) is right_complementable Element of the carrier of c₁
(id the carrier of c₁) . NRM is right_complementable Element of the carrier of c₁
((id the carrier of c₁) . NRM) + UNIT is right_complementable Element of the carrier of c₁
the addF of c₁ . (((id the carrier of c₁) . NRM),UNIT) is right_complementable Element of the carrier of c₁
K23(((id the carrier of c₁) . NRM),UNIT) is set
the addF of c₁ . K23(((id the carrier of c₁) . NRM),UNIT) is set
(id the carrier of c₁) . UNIT is right_complementable Element of the carrier of c₁
((id the carrier of c₁) . NRM) + ((id the carrier of c₁) . UNIT) is right_complementable Element of the carrier of c₁
the addF of c₁ . (((id the carrier of c₁) . NRM),((id the carrier of c₁) . UNIT)) is right_complementable Element of the carrier of c₁
K23(((id the carrier of c₁) . NRM),((id the carrier of c₁) . UNIT)) is set
the addF of c₁ . K23(((id the carrier of c₁) . NRM),((id the carrier of c₁) . UNIT)) is set
NRM is right_complementable Element of the carrier of c₁
UNIT is complex set
UNIT * NRM is right_complementable Element of the carrier of c₁
the Mult of c₁ is V13() V16([:COMPLEX, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([:COMPLEX, the carrier of c₁:]) V27([:COMPLEX, the carrier of c₁:], the carrier of c₁) Element of bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:]
[:COMPLEX, the carrier of c₁:] is set
[:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
K23(UNIT,NRM) is set
the Mult of c₁ . K23(UNIT,NRM) is set
(id the carrier of c₁) . (UNIT * NRM) is right_complementable Element of the carrier of c₁
(id the carrier of c₁) . NRM is right_complementable Element of the carrier of c₁
UNIT * ((id the carrier of c₁) . NRM) is right_complementable Element of the carrier of c₁
K23(UNIT,((id the carrier of c₁) . NRM)) is set
the Mult of c₁ . K23(UNIT,((id the carrier of c₁) . NRM)) is set
NRM is right_complementable Element of the carrier of c₁
(id the carrier of c₁) . NRM is right_complementable Element of the carrier of c₁
||.((id the carrier of c₁) . NRM).|| is complex real ext-real Element of REAL
the normF of c₁ is non empty V13() V16( the carrier of c₁) V17( REAL ) Function-like V23( the carrier of c₁) V27( the carrier of c₁, REAL ) V35() V36() V37() Element of bool [: the carrier of c₁,REAL:]
[: the carrier of c₁,REAL:] is V35() V36() V37() set
bool [: the carrier of c₁,REAL:] is set
the normF of c₁ . ((id the carrier of c₁) . NRM) is complex real ext-real Element of REAL
||.NRM.|| is complex real ext-real Element of REAL
the normF of c₁ . NRM is complex real ext-real Element of REAL
1 * ||.NRM.|| is complex real ext-real Element of REAL
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
MULT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
NRM is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,UNIT,NRM) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
ADD is right_complementable Element of the carrier of c₁
(c₁,UNIT,NRM) . ADD is right_complementable Element of the carrier of c₁
UNIT . ADD is right_complementable Element of the carrier of c₁
NRM . (UNIT . ADD) is right_complementable Element of the carrier of c₁
MULT . ADD is right_complementable Element of the carrier of c₁
ADD is right_complementable Element of the carrier of c₁
MULT . ADD is right_complementable Element of the carrier of c₁
UNIT . ADD is right_complementable Element of the carrier of c₁
NRM . (UNIT . ADD) is right_complementable Element of the carrier of c₁
BS is right_complementable Element of the carrier of c₁
MULT . BS is right_complementable Element of the carrier of c₁
UNIT . BS is right_complementable Element of the carrier of c₁
NRM . (UNIT . BS) is right_complementable Element of the carrier of c₁
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
MULT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,MULT,UNIT) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
NRM is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,MULT,UNIT),NRM) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,UNIT,NRM) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,MULT,(c₁,UNIT,NRM)) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
ADD is right_complementable Element of the carrier of c₁
(c₁,(c₁,MULT,UNIT),NRM) . ADD is right_complementable Element of the carrier of c₁
(c₁,MULT,UNIT) . ADD is right_complementable Element of the carrier of c₁
NRM . ((c₁,MULT,UNIT) . ADD) is right_complementable Element of the carrier of c₁
MULT . ADD is right_complementable Element of the carrier of c₁
UNIT . (MULT . ADD) is right_complementable Element of the carrier of c₁
NRM . (UNIT . (MULT . ADD)) is right_complementable Element of the carrier of c₁
(c₁,UNIT,NRM) . (MULT . ADD) is right_complementable Element of the carrier of c₁
(c₁,MULT,(c₁,UNIT,NRM)) . ADD is right_complementable Element of the carrier of c₁
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty set
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
UNIT * (id the carrier of c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
(id the carrier of c₁) * UNIT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
MULT is right_complementable Element of the carrier of c₁
((id the carrier of c₁) * UNIT) . MULT is right_complementable Element of the carrier of c₁
NRM is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,UNIT,NRM) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,UNIT,NRM) . MULT is right_complementable Element of the carrier of c₁
UNIT . MULT is right_complementable Element of the carrier of c₁
NRM . (UNIT . MULT) is right_complementable Element of the carrier of c₁
MULT is right_complementable Element of the carrier of c₁
(UNIT * (id the carrier of c₁)) . MULT is right_complementable Element of the carrier of c₁
(c₁,NRM,UNIT) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,NRM,UNIT) . MULT is right_complementable Element of the carrier of c₁
NRM . MULT is right_complementable Element of the carrier of c₁
UNIT . (NRM . MULT) is right_complementable Element of the carrier of c₁
UNIT . MULT is right_complementable Element of the carrier of c₁
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
MULT is Element of BoundedLinearOperators (c₁,c₁)
UNIT is Element of BoundedLinearOperators (c₁,c₁)
(c₁,MULT,UNIT) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (MULT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
NRM is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁,MULT,UNIT),NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,MULT,UNIT),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,MULT,UNIT),c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,UNIT,NRM) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,MULT,(c₁,UNIT,NRM)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,UNIT,NRM),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (MULT,c₁,c₁)),(modetrans ((c₁,UNIT,NRM),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (MULT,c₁,c₁)),(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
NRM is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁),NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,NRM,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((id the carrier of c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
UNIT is Element of BoundedLinearOperators (c₁,c₁)
MULT is Element of BoundedLinearOperators (c₁,c₁)
(c₁,UNIT,MULT) is Element of BoundedLinearOperators (c₁,c₁)
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (UNIT,MULT) is Element of BoundedLinearOperators (c₁,c₁)
K23(UNIT,MULT) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(UNIT,MULT) is set
NRM is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁,UNIT,MULT),NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,UNIT,MULT),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,UNIT,MULT),c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,UNIT,NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,MULT,NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (MULT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,UNIT,NRM),(c₁,MULT,NRM)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,UNIT,NRM),(c₁,MULT,NRM)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,UNIT,NRM),(c₁,MULT,NRM)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,UNIT,NRM),(c₁,MULT,NRM)) is set
C_NormSpace_of_BoundedLinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
CNORMSTR(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁)) #) is non empty strict CNORMSTR
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))),(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is set
K23((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))),(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))),(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is set
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
n is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans ((c₁,UNIT,MULT),c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx) + ((c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx) is right_complementable Element of the carrier of c₁
the addF of c₁ is V13() V16([: the carrier of c₁, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([: the carrier of c₁, the carrier of c₁:]) V27([: the carrier of c₁, the carrier of c₁:], the carrier of c₁) Element of bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:]
[:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
the addF of c₁ . (((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx),((c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx)) is right_complementable Element of the carrier of c₁
K23(((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx),((c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx)) is set
the addF of c₁ . K23(((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx),((c₁,(modetrans (MULT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx)) is set
n + m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (n,m) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23(n,m) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(n,m) is set
(modetrans ((c₁,UNIT,MULT),c₁,c₁)) . xx is right_complementable Element of the carrier of c₁
(modetrans (UNIT,c₁,c₁)) . xx is right_complementable Element of the carrier of c₁
(modetrans (MULT,c₁,c₁)) . xx is right_complementable Element of the carrier of c₁
((modetrans (UNIT,c₁,c₁)) . xx) + ((modetrans (MULT,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
the addF of c₁ . (((modetrans (UNIT,c₁,c₁)) . xx),((modetrans (MULT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
K23(((modetrans (UNIT,c₁,c₁)) . xx),((modetrans (MULT,c₁,c₁)) . xx)) is set
the addF of c₁ . K23(((modetrans (UNIT,c₁,c₁)) . xx),((modetrans (MULT,c₁,c₁)) . xx)) is set
(modetrans (NRM,c₁,c₁)) . ((modetrans ((c₁,UNIT,MULT),c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
(modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
(modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)) + ((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
the addF of c₁ . (((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)),((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx))) is right_complementable Element of the carrier of c₁
K23(((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)),((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx))) is set
the addF of c₁ . K23(((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)),((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx))) is set
((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx) + ((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
the addF of c₁ . (((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx),((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx))) is right_complementable Element of the carrier of c₁
K23(((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx),((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx))) is set
the addF of c₁ . K23(((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx),((modetrans (NRM,c₁,c₁)) . ((modetrans (MULT,c₁,c₁)) . xx))) is set
r is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
g is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
g + g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (g,g1) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23(g,g1) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(g,g1) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
NRM is Element of BoundedLinearOperators (c₁,c₁)
UNIT is Element of BoundedLinearOperators (c₁,c₁)
MULT is Element of BoundedLinearOperators (c₁,c₁)
(c₁,UNIT,MULT) is Element of BoundedLinearOperators (c₁,c₁)
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (UNIT,MULT) is Element of BoundedLinearOperators (c₁,c₁)
K23(UNIT,MULT) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(UNIT,MULT) is set
(c₁,NRM,(c₁,UNIT,MULT)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans ((c₁,UNIT,MULT),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans ((c₁,UNIT,MULT),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,NRM,UNIT) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,NRM,MULT) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (MULT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,NRM,UNIT),(c₁,NRM,MULT)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,NRM,UNIT),(c₁,NRM,MULT)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,NRM,UNIT),(c₁,NRM,MULT)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,NRM,UNIT),(c₁,NRM,MULT)) is set
C_NormSpace_of_BoundedLinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
CNORMSTR(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁)) #) is non empty strict CNORMSTR
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))),(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁)))) is set
K23((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))),(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁)))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))),(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁)))) is set
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
n is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans ((c₁,UNIT,MULT),c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx) + ((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁))) . xx) is right_complementable Element of the carrier of c₁
the addF of c₁ is V13() V16([: the carrier of c₁, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([: the carrier of c₁, the carrier of c₁:]) V27([: the carrier of c₁, the carrier of c₁:], the carrier of c₁) Element of bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:]
[:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
bool [:[: the carrier of c₁, the carrier of c₁:], the carrier of c₁:] is set
the addF of c₁ . (((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx),((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁))) . xx)) is right_complementable Element of the carrier of c₁
K23(((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx),((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁))) . xx)) is set
the addF of c₁ . K23(((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx),((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (MULT,c₁,c₁))) . xx)) is set
n + m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (n,m) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23(n,m) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(n,m) is set
(modetrans (NRM,c₁,c₁)) . xx is right_complementable Element of the carrier of c₁
(modetrans ((c₁,UNIT,MULT),c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
(modetrans (UNIT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
(modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
((modetrans (UNIT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx)) + ((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
the addF of c₁ . (((modetrans (UNIT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx)),((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx))) is right_complementable Element of the carrier of c₁
K23(((modetrans (UNIT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx)),((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx))) is set
the addF of c₁ . K23(((modetrans (UNIT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx)),((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx))) is set
((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx) + ((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
the addF of c₁ . (((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx),((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx))) is right_complementable Element of the carrier of c₁
K23(((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx),((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx))) is set
the addF of c₁ . K23(((c₁,(modetrans (NRM,c₁,c₁)),(modetrans (UNIT,c₁,c₁))) . xx),((modetrans (MULT,c₁,c₁)) . ((modetrans (NRM,c₁,c₁)) . xx))) is set
r is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
g is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
g + g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (g,g1) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23(g,g1) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(g,g1) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
UNIT is Element of BoundedLinearOperators (c₁,c₁)
NRM is Element of BoundedLinearOperators (c₁,c₁)
(c₁,UNIT,NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
MULT is complex set
ADD is complex set
MULT * ADD is complex set
(c₁,(c₁,UNIT,NRM),(MULT * ADD)) is Element of BoundedLinearOperators (c₁,c₁)
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((MULT * ADD),(c₁,UNIT,NRM)) is set
K23((MULT * ADD),(c₁,UNIT,NRM)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((MULT * ADD),(c₁,UNIT,NRM)) is set
(c₁,UNIT,ADD) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (ADD,UNIT) is set
K23(ADD,UNIT) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(ADD,UNIT) is set
(c₁,NRM,MULT) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (MULT,NRM) is set
K23(MULT,NRM) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(MULT,NRM) is set
(c₁,(c₁,UNIT,ADD),(c₁,NRM,MULT)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,UNIT,ADD),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁,NRM,MULT),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,UNIT,ADD),c₁,c₁)),(modetrans ((c₁,NRM,MULT),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
C_NormSpace_of_BoundedLinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
CNORMSTR(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁)) #) is non empty strict CNORMSTR
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((MULT * ADD),(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is set
K23((MULT * ADD),(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((MULT * ADD),(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁)))) is set
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
n is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans ((c₁,UNIT,ADD),c₁,c₁)),(modetrans ((c₁,NRM,MULT),c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx is right_complementable Element of the carrier of c₁
(MULT * ADD) * ((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx) is right_complementable Element of the carrier of c₁
the Mult of c₁ is V13() V16([:COMPLEX, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([:COMPLEX, the carrier of c₁:]) V27([:COMPLEX, the carrier of c₁:], the carrier of c₁) Element of bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:]
[:COMPLEX, the carrier of c₁:] is set
[:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
K23((MULT * ADD),((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx)) is set
the Mult of c₁ . K23((MULT * ADD),((c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) . xx)) is set
(modetrans (UNIT,c₁,c₁)) . xx is right_complementable Element of the carrier of c₁
ADD * ((modetrans (UNIT,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
K23(ADD,((modetrans (UNIT,c₁,c₁)) . xx)) is set
the Mult of c₁ . K23(ADD,((modetrans (UNIT,c₁,c₁)) . xx)) is set
MULT * m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
K23(MULT,m) is set
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(MULT,m) is set
(modetrans ((c₁,NRM,MULT),c₁,c₁)) . (ADD * ((modetrans (UNIT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
(modetrans (NRM,c₁,c₁)) . (ADD * ((modetrans (UNIT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
MULT * ((modetrans (NRM,c₁,c₁)) . (ADD * ((modetrans (UNIT,c₁,c₁)) . xx))) is right_complementable Element of the carrier of c₁
K23(MULT,((modetrans (NRM,c₁,c₁)) . (ADD * ((modetrans (UNIT,c₁,c₁)) . xx)))) is set
the Mult of c₁ . K23(MULT,((modetrans (NRM,c₁,c₁)) . (ADD * ((modetrans (UNIT,c₁,c₁)) . xx)))) is set
ADD * n is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23(ADD,n) is set
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(ADD,n) is set
(modetrans ((c₁,UNIT,ADD),c₁,c₁)) . xx is right_complementable Element of the carrier of c₁
(modetrans ((c₁,NRM,MULT),c₁,c₁)) . ((modetrans ((c₁,UNIT,ADD),c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
(modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx) is right_complementable Element of the carrier of c₁
ADD * ((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
K23(ADD,((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx))) is set
the Mult of c₁ . K23(ADD,((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx))) is set
MULT * (ADD * ((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx))) is right_complementable Element of the carrier of c₁
K23(MULT,(ADD * ((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)))) is set
the Mult of c₁ . K23(MULT,(ADD * ((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)))) is set
(MULT * ADD) * ((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx)) is right_complementable Element of the carrier of c₁
K23((MULT * ADD),((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx))) is set
the Mult of c₁ . K23((MULT * ADD),((modetrans (NRM,c₁,c₁)) . ((modetrans (UNIT,c₁,c₁)) . xx))) is set
g is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
r is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
(MULT * ADD) * r is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
K23((MULT * ADD),r) is set
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23((MULT * ADD),r) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
UNIT is Element of BoundedLinearOperators (c₁,c₁)
NRM is Element of BoundedLinearOperators (c₁,c₁)
(c₁,UNIT,NRM) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (UNIT,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
modetrans (NRM,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans (NRM,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
MULT is complex set
(c₁,(c₁,UNIT,NRM),MULT) is Element of BoundedLinearOperators (c₁,c₁)
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (MULT,(c₁,UNIT,NRM)) is set
K23(MULT,(c₁,UNIT,NRM)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(MULT,(c₁,UNIT,NRM)) is set
(c₁,NRM,MULT) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (MULT,NRM) is set
K23(MULT,NRM) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(MULT,NRM) is set
(c₁,UNIT,(c₁,NRM,MULT)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,NRM,MULT),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (UNIT,c₁,c₁)),(modetrans ((c₁,NRM,MULT),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
(c₁,UNIT,1r) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (1r,UNIT) is set
K23(1r,UNIT) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(1r,UNIT) is set
BS is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
1r * BS is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
K23(1r,BS) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(1r,BS) is set
MULT * 1r is complex set
(c₁,(c₁,UNIT,NRM),(MULT * 1r)) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((MULT * 1r),(c₁,UNIT,NRM)) is set
K23((MULT * 1r),(c₁,UNIT,NRM)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((MULT * 1r),(c₁,UNIT,NRM)) is set
(c₁,(c₁,UNIT,1r),(c₁,NRM,MULT)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,UNIT,1r),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,UNIT,1r),c₁,c₁)),(modetrans ((c₁,NRM,MULT),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
the carrier of (c₁) is non empty set
UNIT is Element of the carrier of (c₁)
MULT is Element of the carrier of (c₁)
UNIT * MULT is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
K23(UNIT,MULT) is set
the multF of (c₁) . K23(UNIT,MULT) is set
ADD is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁),ADD) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (ADD,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (ADD,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
MULT * UNIT is Element of the carrier of (c₁)
the multF of (c₁) . (MULT,UNIT) is Element of the carrier of (c₁)
K23(MULT,UNIT) is set
the multF of (c₁) . K23(MULT,UNIT) is set
(c₁,ADD,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (ADD,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
the carrier of (c₁) is non empty set
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
UNIT * NRM is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the multF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
NRM * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,MULT) is Element of the carrier of (c₁)
K23(NRM,MULT) is set
the multF of (c₁) . K23(NRM,MULT) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict unital doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
the carrier of (c₁) is non empty set
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
1. (c₁) is Element of the carrier of (c₁)
the OneF of (c₁) is Element of the carrier of (c₁)
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
NRM + UNIT is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
K23(NRM,UNIT) is set
the addF of (c₁) . K23(NRM,UNIT) is set
UNIT + NRM is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the addF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
(NRM + UNIT) + MULT is Element of the carrier of (c₁)
the addF of (c₁) . ((NRM + UNIT),MULT) is Element of the carrier of (c₁)
K23((NRM + UNIT),MULT) is set
the addF of (c₁) . K23((NRM + UNIT),MULT) is set
UNIT + MULT is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
K23(UNIT,MULT) is set
the addF of (c₁) . K23(UNIT,MULT) is set
NRM + (UNIT + MULT) is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,(UNIT + MULT)) is Element of the carrier of (c₁)
K23(NRM,(UNIT + MULT)) is set
the addF of (c₁) . K23(NRM,(UNIT + MULT)) is set
NRM + (0. (c₁)) is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,(0. (c₁))) is Element of the carrier of (c₁)
K23(NRM,(0. (c₁))) is set
the addF of (c₁) . K23(NRM,(0. (c₁))) is set
NRM * UNIT is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
the multF of (c₁) . K23(NRM,UNIT) is set
(NRM * UNIT) * MULT is Element of the carrier of (c₁)
the multF of (c₁) . ((NRM * UNIT),MULT) is Element of the carrier of (c₁)
K23((NRM * UNIT),MULT) is set
the multF of (c₁) . K23((NRM * UNIT),MULT) is set
UNIT * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
the multF of (c₁) . K23(UNIT,MULT) is set
NRM * (UNIT * MULT) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(UNIT * MULT)) is Element of the carrier of (c₁)
K23(NRM,(UNIT * MULT)) is set
the multF of (c₁) . K23(NRM,(UNIT * MULT)) is set
NRM * (1. (c₁)) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(1. (c₁))) is Element of the carrier of (c₁)
K23(NRM,(1. (c₁))) is set
the multF of (c₁) . K23(NRM,(1. (c₁))) is set
(1. (c₁)) * NRM is Element of the carrier of (c₁)
the multF of (c₁) . ((1. (c₁)),NRM) is Element of the carrier of (c₁)
K23((1. (c₁)),NRM) is set
the multF of (c₁) . K23((1. (c₁)),NRM) is set
NRM * (UNIT + MULT) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(UNIT + MULT)) is Element of the carrier of (c₁)
the multF of (c₁) . K23(NRM,(UNIT + MULT)) is set
NRM * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,MULT) is Element of the carrier of (c₁)
K23(NRM,MULT) is set
the multF of (c₁) . K23(NRM,MULT) is set
(NRM * UNIT) + (NRM * MULT) is Element of the carrier of (c₁)
the addF of (c₁) . ((NRM * UNIT),(NRM * MULT)) is Element of the carrier of (c₁)
K23((NRM * UNIT),(NRM * MULT)) is set
the addF of (c₁) . K23((NRM * UNIT),(NRM * MULT)) is set
(UNIT + MULT) * NRM is Element of the carrier of (c₁)
the multF of (c₁) . ((UNIT + MULT),NRM) is Element of the carrier of (c₁)
K23((UNIT + MULT),NRM) is set
the multF of (c₁) . K23((UNIT + MULT),NRM) is set
UNIT * NRM is Element of the carrier of (c₁)
the multF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
the multF of (c₁) . K23(UNIT,NRM) is set
MULT * NRM is Element of the carrier of (c₁)
the multF of (c₁) . (MULT,NRM) is Element of the carrier of (c₁)
K23(MULT,NRM) is set
the multF of (c₁) . K23(MULT,NRM) is set
(UNIT * NRM) + (MULT * NRM) is Element of the carrier of (c₁)
the addF of (c₁) . ((UNIT * NRM),(MULT * NRM)) is Element of the carrier of (c₁)
K23((UNIT * NRM),(MULT * NRM)) is set
the addF of (c₁) . K23((UNIT * NRM),(MULT * NRM)) is set
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g1 + g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,g) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,g) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,g) is set
r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
(g1 + g) + r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((g1 + g),r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((g1 + g),r) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((g1 + g),r) is set
g + r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g,r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g,r) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g,r) is set
g1 + (g + r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,(g + r)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,(g + r)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,(g + r)) is set
0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is zero right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the ZeroF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g1 + (0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g1 + m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,m) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,m) is set
n is Element of the carrier of (c₁)
NRM + n is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,n) is Element of the carrier of (c₁)
K23(NRM,n) is set
the addF of (c₁) . K23(NRM,n) is set
n is Element of BoundedLinearOperators (c₁,c₁)
m is Element of BoundedLinearOperators (c₁,c₁)
(c₁,n,m) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (n,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (m,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (n,c₁,c₁)),(modetrans (m,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
xx is Element of BoundedLinearOperators (c₁,c₁)
(c₁) . ((c₁,n,m),xx) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,n,m),xx) is set
(c₁) . K23((c₁,n,m),xx) is set
(c₁,xx,(c₁,n,m)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (xx,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁,n,m),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (xx,c₁,c₁)),(modetrans ((c₁,n,m),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,n) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans (n,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,xx,n),m) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,xx,n),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,xx,n),c₁,c₁)),(modetrans (m,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁) . (m,(c₁,xx,n)) is Element of BoundedLinearOperators (c₁,c₁)
K23(m,(c₁,xx,n)) is set
(c₁) . K23(m,(c₁,xx,n)) is set
(c₁,(c₁),m) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (m,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,m,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (m,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,n,xx) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (n,xx) is Element of BoundedLinearOperators (c₁,c₁)
K23(n,xx) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(n,xx) is set
(c₁,(c₁,n,xx),m) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,n,xx),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,n,xx),c₁,c₁)),(modetrans (m,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,m) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans (m,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,n,m),(c₁,xx,m)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,n,m),(c₁,xx,m)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,n,m),(c₁,xx,m)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,n,m),(c₁,xx,m)) is set
(c₁) . (m,xx) is Element of BoundedLinearOperators (c₁,c₁)
K23(m,xx) is set
(c₁) . K23(m,xx) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,n,m),((c₁) . (m,xx))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,n,m),((c₁) . (m,xx))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,n,m),((c₁) . (m,xx))) is set
(c₁,m,(c₁,n,xx)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (m,c₁,c₁)),(modetrans ((c₁,n,xx),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,m,n) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (m,c₁,c₁)),(modetrans (n,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,m,xx) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (m,c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,m,n),(c₁,m,xx)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,m,n),(c₁,m,xx)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,m,n),(c₁,m,xx)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,m,n),(c₁,m,xx)) is set
(c₁) . (xx,m) is Element of BoundedLinearOperators (c₁,c₁)
K23(xx,m) is set
(c₁) . K23(xx,m) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,m,n),((c₁) . (xx,m))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,m,n),((c₁) . (xx,m))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,m,n),((c₁) . (xx,m))) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict unital doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
the carrier of (c₁) is non empty set
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
1. (c₁) is Element of the carrier of (c₁)
the OneF of (c₁) is Element of the carrier of (c₁)
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
NRM + UNIT is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
K23(NRM,UNIT) is set
the addF of (c₁) . K23(NRM,UNIT) is set
UNIT + NRM is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the addF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
ADD is Element of the carrier of (c₁)
MULT + ADD is Element of the carrier of (c₁)
the addF of (c₁) . (MULT,ADD) is Element of the carrier of (c₁)
K23(MULT,ADD) is set
the addF of (c₁) . K23(MULT,ADD) is set
BS is Element of the carrier of (c₁)
(MULT + ADD) + BS is Element of the carrier of (c₁)
the addF of (c₁) . ((MULT + ADD),BS) is Element of the carrier of (c₁)
K23((MULT + ADD),BS) is set
the addF of (c₁) . K23((MULT + ADD),BS) is set
ADD + BS is Element of the carrier of (c₁)
the addF of (c₁) . (ADD,BS) is Element of the carrier of (c₁)
K23(ADD,BS) is set
the addF of (c₁) . K23(ADD,BS) is set
MULT + (ADD + BS) is Element of the carrier of (c₁)
the addF of (c₁) . (MULT,(ADD + BS)) is Element of the carrier of (c₁)
K23(MULT,(ADD + BS)) is set
the addF of (c₁) . K23(MULT,(ADD + BS)) is set
BLOP is Element of the carrier of (c₁)
BLOP + (0. (c₁)) is Element of the carrier of (c₁)
the addF of (c₁) . (BLOP,(0. (c₁))) is Element of the carrier of (c₁)
K23(BLOP,(0. (c₁))) is set
the addF of (c₁) . K23(BLOP,(0. (c₁))) is set
RBLOP is Element of the carrier of (c₁)
seq is Element of the carrier of (c₁)
seq1 is Element of the carrier of (c₁)
seq * seq1 is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . (seq,seq1) is Element of the carrier of (c₁)
K23(seq,seq1) is set
the multF of (c₁) . K23(seq,seq1) is set
g1 is Element of the carrier of (c₁)
(seq * seq1) * g1 is Element of the carrier of (c₁)
the multF of (c₁) . ((seq * seq1),g1) is Element of the carrier of (c₁)
K23((seq * seq1),g1) is set
the multF of (c₁) . K23((seq * seq1),g1) is set
seq1 * g1 is Element of the carrier of (c₁)
the multF of (c₁) . (seq1,g1) is Element of the carrier of (c₁)
K23(seq1,g1) is set
the multF of (c₁) . K23(seq1,g1) is set
seq * (seq1 * g1) is Element of the carrier of (c₁)
the multF of (c₁) . (seq,(seq1 * g1)) is Element of the carrier of (c₁)
K23(seq,(seq1 * g1)) is set
the multF of (c₁) . K23(seq,(seq1 * g1)) is set
g is Element of the carrier of (c₁)
g * (1. (c₁)) is Element of the carrier of (c₁)
the multF of (c₁) . (g,(1. (c₁))) is Element of the carrier of (c₁)
K23(g,(1. (c₁))) is set
the multF of (c₁) . K23(g,(1. (c₁))) is set
r is Element of the carrier of (c₁)
(1. (c₁)) * r is Element of the carrier of (c₁)
the multF of (c₁) . ((1. (c₁)),r) is Element of the carrier of (c₁)
K23((1. (c₁)),r) is set
the multF of (c₁) . K23((1. (c₁)),r) is set
m is Element of the carrier of (c₁)
n is Element of the carrier of (c₁)
xx is Element of the carrier of (c₁)
n + xx is Element of the carrier of (c₁)
the addF of (c₁) . (n,xx) is Element of the carrier of (c₁)
K23(n,xx) is set
the addF of (c₁) . K23(n,xx) is set
m * (n + xx) is Element of the carrier of (c₁)
the multF of (c₁) . (m,(n + xx)) is Element of the carrier of (c₁)
K23(m,(n + xx)) is set
the multF of (c₁) . K23(m,(n + xx)) is set
m * n is Element of the carrier of (c₁)
the multF of (c₁) . (m,n) is Element of the carrier of (c₁)
K23(m,n) is set
the multF of (c₁) . K23(m,n) is set
m * xx is Element of the carrier of (c₁)
the multF of (c₁) . (m,xx) is Element of the carrier of (c₁)
K23(m,xx) is set
the multF of (c₁) . K23(m,xx) is set
(m * n) + (m * xx) is Element of the carrier of (c₁)
the addF of (c₁) . ((m * n),(m * xx)) is Element of the carrier of (c₁)
K23((m * n),(m * xx)) is set
the addF of (c₁) . K23((m * n),(m * xx)) is set
zz is Element of the carrier of (c₁)
c₁₉ is Element of the carrier of (c₁)
zz + c₁₉ is Element of the carrier of (c₁)
the addF of (c₁) . (zz,c₁₉) is Element of the carrier of (c₁)
K23(zz,c₁₉) is set
the addF of (c₁) . K23(zz,c₁₉) is set
yy is Element of the carrier of (c₁)
(zz + c₁₉) * yy is Element of the carrier of (c₁)
the multF of (c₁) . ((zz + c₁₉),yy) is Element of the carrier of (c₁)
K23((zz + c₁₉),yy) is set
the multF of (c₁) . K23((zz + c₁₉),yy) is set
zz * yy is Element of the carrier of (c₁)
the multF of (c₁) . (zz,yy) is Element of the carrier of (c₁)
K23(zz,yy) is set
the multF of (c₁) . K23(zz,yy) is set
c₁₉ * yy is Element of the carrier of (c₁)
the multF of (c₁) . (c₁₉,yy) is Element of the carrier of (c₁)
K23(c₁₉,yy) is set
the multF of (c₁) . K23(c₁₉,yy) is set
(zz * yy) + (c₁₉ * yy) is Element of the carrier of (c₁)
the addF of (c₁) . ((zz * yy),(c₁₉ * yy)) is Element of the carrier of (c₁)
K23((zz * yy),(c₁₉ * yy)) is set
the addF of (c₁) . K23((zz * yy),(c₁₉ * yy)) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict unital doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
the carrier of (c₁) is non empty set
UNIT is Element of the carrier of (c₁)
MULT is Element of the carrier of (c₁)
UNIT * MULT is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
K23(UNIT,MULT) is set
the multF of (c₁) . K23(UNIT,MULT) is set
ADD is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁),ADD) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (ADD,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (ADD,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
MULT * UNIT is Element of the carrier of (c₁)
the multF of (c₁) . (MULT,UNIT) is Element of the carrier of (c₁)
K23(MULT,UNIT) is set
the multF of (c₁) . K23(MULT,UNIT) is set
(c₁,ADD,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (ADD,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty strict ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
the carrier of (c₁) is non empty set
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
UNIT * NRM is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the multF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
NRM * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,MULT) is Element of the carrier of (c₁)
K23(NRM,MULT) is set
the multF of (c₁) . K23(NRM,MULT) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty unital strict ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
the carrier of (c₁) is non empty set
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
1. (c₁) is Element of the carrier of (c₁)
the OneF of (c₁) is Element of the carrier of (c₁)
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
NRM + UNIT is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
K23(NRM,UNIT) is set
the addF of (c₁) . K23(NRM,UNIT) is set
UNIT + NRM is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the addF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
(NRM + UNIT) + MULT is Element of the carrier of (c₁)
the addF of (c₁) . ((NRM + UNIT),MULT) is Element of the carrier of (c₁)
K23((NRM + UNIT),MULT) is set
the addF of (c₁) . K23((NRM + UNIT),MULT) is set
UNIT + MULT is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
K23(UNIT,MULT) is set
the addF of (c₁) . K23(UNIT,MULT) is set
NRM + (UNIT + MULT) is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,(UNIT + MULT)) is Element of the carrier of (c₁)
K23(NRM,(UNIT + MULT)) is set
the addF of (c₁) . K23(NRM,(UNIT + MULT)) is set
NRM + (0. (c₁)) is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,(0. (c₁))) is Element of the carrier of (c₁)
K23(NRM,(0. (c₁))) is set
the addF of (c₁) . K23(NRM,(0. (c₁))) is set
NRM * UNIT is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
the multF of (c₁) . K23(NRM,UNIT) is set
(NRM * UNIT) * MULT is Element of the carrier of (c₁)
the multF of (c₁) . ((NRM * UNIT),MULT) is Element of the carrier of (c₁)
K23((NRM * UNIT),MULT) is set
the multF of (c₁) . K23((NRM * UNIT),MULT) is set
UNIT * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
the multF of (c₁) . K23(UNIT,MULT) is set
NRM * (UNIT * MULT) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(UNIT * MULT)) is Element of the carrier of (c₁)
K23(NRM,(UNIT * MULT)) is set
the multF of (c₁) . K23(NRM,(UNIT * MULT)) is set
NRM * (1. (c₁)) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(1. (c₁))) is Element of the carrier of (c₁)
K23(NRM,(1. (c₁))) is set
the multF of (c₁) . K23(NRM,(1. (c₁))) is set
(1. (c₁)) * NRM is Element of the carrier of (c₁)
the multF of (c₁) . ((1. (c₁)),NRM) is Element of the carrier of (c₁)
K23((1. (c₁)),NRM) is set
the multF of (c₁) . K23((1. (c₁)),NRM) is set
NRM * (UNIT + MULT) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(UNIT + MULT)) is Element of the carrier of (c₁)
the multF of (c₁) . K23(NRM,(UNIT + MULT)) is set
NRM * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,MULT) is Element of the carrier of (c₁)
K23(NRM,MULT) is set
the multF of (c₁) . K23(NRM,MULT) is set
(NRM * UNIT) + (NRM * MULT) is Element of the carrier of (c₁)
the addF of (c₁) . ((NRM * UNIT),(NRM * MULT)) is Element of the carrier of (c₁)
K23((NRM * UNIT),(NRM * MULT)) is set
the addF of (c₁) . K23((NRM * UNIT),(NRM * MULT)) is set
(UNIT + MULT) * NRM is Element of the carrier of (c₁)
the multF of (c₁) . ((UNIT + MULT),NRM) is Element of the carrier of (c₁)
K23((UNIT + MULT),NRM) is set
the multF of (c₁) . K23((UNIT + MULT),NRM) is set
UNIT * NRM is Element of the carrier of (c₁)
the multF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
the multF of (c₁) . K23(UNIT,NRM) is set
MULT * NRM is Element of the carrier of (c₁)
the multF of (c₁) . (MULT,NRM) is Element of the carrier of (c₁)
K23(MULT,NRM) is set
the multF of (c₁) . K23(MULT,NRM) is set
(UNIT * NRM) + (MULT * NRM) is Element of the carrier of (c₁)
the addF of (c₁) . ((UNIT * NRM),(MULT * NRM)) is Element of the carrier of (c₁)
K23((UNIT * NRM),(MULT * NRM)) is set
the addF of (c₁) . K23((UNIT * NRM),(MULT * NRM)) is set
ADD is complex set
ADD * (NRM * UNIT) is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(ADD,(NRM * UNIT)) is set
the Mult of (c₁) . K23(ADD,(NRM * UNIT)) is set
ADD * NRM is Element of the carrier of (c₁)
K23(ADD,NRM) is set
the Mult of (c₁) . K23(ADD,NRM) is set
(ADD * NRM) * UNIT is Element of the carrier of (c₁)
the multF of (c₁) . ((ADD * NRM),UNIT) is Element of the carrier of (c₁)
K23((ADD * NRM),UNIT) is set
the multF of (c₁) . K23((ADD * NRM),UNIT) is set
ADD * (NRM + UNIT) is Element of the carrier of (c₁)
K23(ADD,(NRM + UNIT)) is set
the Mult of (c₁) . K23(ADD,(NRM + UNIT)) is set
ADD * UNIT is Element of the carrier of (c₁)
K23(ADD,UNIT) is set
the Mult of (c₁) . K23(ADD,UNIT) is set
(ADD * NRM) + (ADD * UNIT) is Element of the carrier of (c₁)
the addF of (c₁) . ((ADD * NRM),(ADD * UNIT)) is Element of the carrier of (c₁)
K23((ADD * NRM),(ADD * UNIT)) is set
the addF of (c₁) . K23((ADD * NRM),(ADD * UNIT)) is set
BS is complex set
ADD + BS is complex set
(ADD + BS) * NRM is Element of the carrier of (c₁)
K23((ADD + BS),NRM) is set
the Mult of (c₁) . K23((ADD + BS),NRM) is set
BS * NRM is Element of the carrier of (c₁)
K23(BS,NRM) is set
the Mult of (c₁) . K23(BS,NRM) is set
(ADD * NRM) + (BS * NRM) is Element of the carrier of (c₁)
the addF of (c₁) . ((ADD * NRM),(BS * NRM)) is Element of the carrier of (c₁)
K23((ADD * NRM),(BS * NRM)) is set
the addF of (c₁) . K23((ADD * NRM),(BS * NRM)) is set
ADD * BS is complex set
(ADD * BS) * NRM is Element of the carrier of (c₁)
K23((ADD * BS),NRM) is set
the Mult of (c₁) . K23((ADD * BS),NRM) is set
ADD * (BS * NRM) is Element of the carrier of (c₁)
K23(ADD,(BS * NRM)) is set
the Mult of (c₁) . K23(ADD,(BS * NRM)) is set
(ADD * BS) * (NRM * UNIT) is Element of the carrier of (c₁)
K23((ADD * BS),(NRM * UNIT)) is set
the Mult of (c₁) . K23((ADD * BS),(NRM * UNIT)) is set
BS * UNIT is Element of the carrier of (c₁)
K23(BS,UNIT) is set
the Mult of (c₁) . K23(BS,UNIT) is set
(ADD * NRM) * (BS * UNIT) is Element of the carrier of (c₁)
the multF of (c₁) . ((ADD * NRM),(BS * UNIT)) is Element of the carrier of (c₁)
K23((ADD * NRM),(BS * UNIT)) is set
the multF of (c₁) . K23((ADD * NRM),(BS * UNIT)) is set
CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
r + m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,m) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,m) is set
n is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
(r + m) + n is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((r + m),n) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((r + m),n) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((r + m),n) is set
m + n is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (m,n) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(m,n) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(m,n) is set
r + (m + n) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,(m + n)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,(m + n)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,(m + n)) is set
0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is zero right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the ZeroF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
r + (0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
xx is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
r + xx is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,xx) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,xx) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,xx) is set
yy is Element of the carrier of (c₁)
NRM + yy is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,yy) is Element of the carrier of (c₁)
K23(NRM,yy) is set
the addF of (c₁) . K23(NRM,yy) is set
yy is Element of BoundedLinearOperators (c₁,c₁)
xx is Element of BoundedLinearOperators (c₁,c₁)
(c₁,yy,xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (yy,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (xx,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (yy,c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
zz is Element of BoundedLinearOperators (c₁,c₁)
(c₁) . ((c₁,yy,xx),zz) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,yy,xx),zz) is set
(c₁) . K23((c₁,yy,xx),zz) is set
(c₁,zz,(c₁,yy,xx)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (zz,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁,yy,xx),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (zz,c₁,c₁)),(modetrans ((c₁,yy,xx),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,zz,yy) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (zz,c₁,c₁)),(modetrans (yy,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,zz,yy),xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,zz,yy),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,zz,yy),c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁) . (xx,(c₁,zz,yy)) is Element of BoundedLinearOperators (c₁,c₁)
K23(xx,(c₁,zz,yy)) is set
(c₁) . K23(xx,(c₁,zz,yy)) is set
(c₁,(c₁),xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,yy,zz) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (yy,zz) is Element of BoundedLinearOperators (c₁,c₁)
K23(yy,zz) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(yy,zz) is set
(c₁,(c₁,yy,zz),xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,yy,zz),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,yy,zz),c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,zz,xx) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (zz,c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,yy,xx),(c₁,zz,xx)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,yy,xx),(c₁,zz,xx)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,yy,xx),(c₁,zz,xx)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,yy,xx),(c₁,zz,xx)) is set
(c₁) . (xx,zz) is Element of BoundedLinearOperators (c₁,c₁)
K23(xx,zz) is set
(c₁) . K23(xx,zz) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,yy,xx),((c₁) . (xx,zz))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,yy,xx),((c₁) . (xx,zz))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,yy,xx),((c₁) . (xx,zz))) is set
(c₁,xx,(c₁,yy,zz)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans ((c₁,yy,zz),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,yy) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans (yy,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,zz) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans (zz,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,xx,yy),(c₁,xx,zz)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,xx,yy),(c₁,xx,zz)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,xx,yy),(c₁,xx,zz)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,xx,yy),(c₁,xx,zz)) is set
(c₁) . (zz,xx) is Element of BoundedLinearOperators (c₁,c₁)
K23(zz,xx) is set
(c₁) . K23(zz,xx) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,xx,yy),((c₁) . (zz,xx))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,xx,yy),((c₁) . (zz,xx))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,xx,yy),((c₁) . (zz,xx))) is set
(c₁,(c₁,yy,xx),ADD) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (ADD,(c₁,yy,xx)) is set
K23(ADD,(c₁,yy,xx)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(ADD,(c₁,yy,xx)) is set
(c₁,xx,ADD) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (ADD,xx) is set
K23(ADD,xx) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(ADD,xx) is set
(c₁,yy,(c₁,xx,ADD)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,xx,ADD),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (yy,c₁,c₁)),(modetrans ((c₁,xx,ADD),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
ADD * (r + m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
K23(ADD,(r + m)) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,(r + m)) is set
ADD * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(ADD,r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,r) is set
ADD * m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(ADD,m) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,m) is set
(ADD * r) + (ADD * m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((ADD * r),(ADD * m)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD * r),(ADD * m)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD * r),(ADD * m)) is set
(ADD + BS) * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD + BS),r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD + BS),r) is set
BS * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(BS,r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(BS,r) is set
(ADD * r) + (BS * r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((ADD * r),(BS * r)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD * r),(BS * r)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD * r),(BS * r)) is set
(ADD * BS) * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD * BS),r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD * BS),r) is set
ADD * (BS * r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(ADD,(BS * r)) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,(BS * r)) is set
(c₁,(c₁,yy,xx),(ADD * BS)) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((ADD * BS),(c₁,yy,xx)) is set
K23((ADD * BS),(c₁,yy,xx)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((ADD * BS),(c₁,yy,xx)) is set
(c₁,yy,BS) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (BS,yy) is set
K23(BS,yy) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(BS,yy) is set
(c₁,(c₁,yy,BS),(c₁,xx,ADD)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,yy,BS),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,yy,BS),c₁,c₁)),(modetrans ((c₁,xx,ADD),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty unital strict ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
seq is Element of the carrier of (c₁)
RBLOP + seq is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (RBLOP,seq) is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the addF of (c₁) . K23(RBLOP,seq) is set
seq + RBLOP is Element of the carrier of (c₁)
the addF of (c₁) . (seq,RBLOP) is Element of the carrier of (c₁)
K23(seq,RBLOP) is set
the addF of (c₁) . K23(seq,RBLOP) is set
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
seq1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
seq1 + g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (seq1,g1) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(seq1,g1) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(seq1,g1) is set
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
seq is Element of the carrier of (c₁)
RBLOP + seq is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (RBLOP,seq) is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the addF of (c₁) . K23(RBLOP,seq) is set
seq1 is Element of the carrier of (c₁)
(RBLOP + seq) + seq1 is Element of the carrier of (c₁)
the addF of (c₁) . ((RBLOP + seq),seq1) is Element of the carrier of (c₁)
K23((RBLOP + seq),seq1) is set
the addF of (c₁) . K23((RBLOP + seq),seq1) is set
seq + seq1 is Element of the carrier of (c₁)
the addF of (c₁) . (seq,seq1) is Element of the carrier of (c₁)
K23(seq,seq1) is set
the addF of (c₁) . K23(seq,seq1) is set
RBLOP + (seq + seq1) is Element of the carrier of (c₁)
the addF of (c₁) . (RBLOP,(seq + seq1)) is Element of the carrier of (c₁)
K23(RBLOP,(seq + seq1)) is set
the addF of (c₁) . K23(RBLOP,(seq + seq1)) is set
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g1 + g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,g) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,g) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,g) is set
r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
(g1 + g) + r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((g1 + g),r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((g1 + g),r) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((g1 + g),r) is set
g + r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g,r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g,r) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g,r) is set
g1 + (g + r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,(g + r)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,(g + r)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,(g + r)) is set
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
RBLOP + (0. (c₁)) is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (RBLOP,(0. (c₁))) is Element of the carrier of (c₁)
K23(RBLOP,(0. (c₁))) is set
the addF of (c₁) . K23(RBLOP,(0. (c₁))) is set
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
seq is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is zero right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the ZeroF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
seq + (0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (seq,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(seq,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(seq,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
seq is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is zero right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the ZeroF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
seq1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
seq + seq1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (seq,seq1) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(seq,seq1) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(seq,seq1) is set
g1 is Element of the carrier of (c₁)
RBLOP + g1 is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (RBLOP,g1) is Element of the carrier of (c₁)
K23(RBLOP,g1) is set
the addF of (c₁) . K23(RBLOP,g1) is set
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
seq is Element of the carrier of (c₁)
RBLOP * seq is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (RBLOP,seq) is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the multF of (c₁) . K23(RBLOP,seq) is set
seq1 is Element of the carrier of (c₁)
(RBLOP * seq) * seq1 is Element of the carrier of (c₁)
the multF of (c₁) . ((RBLOP * seq),seq1) is Element of the carrier of (c₁)
K23((RBLOP * seq),seq1) is set
the multF of (c₁) . K23((RBLOP * seq),seq1) is set
seq * seq1 is Element of the carrier of (c₁)
the multF of (c₁) . (seq,seq1) is Element of the carrier of (c₁)
K23(seq,seq1) is set
the multF of (c₁) . K23(seq,seq1) is set
RBLOP * (seq * seq1) is Element of the carrier of (c₁)
the multF of (c₁) . (RBLOP,(seq * seq1)) is Element of the carrier of (c₁)
K23(RBLOP,(seq * seq1)) is set
the multF of (c₁) . K23(RBLOP,(seq * seq1)) is set
g is Element of BoundedLinearOperators (c₁,c₁)
g1 is Element of BoundedLinearOperators (c₁,c₁)
(c₁,g,g1) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (g,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (g1,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
r is Element of BoundedLinearOperators (c₁,c₁)
(c₁) . ((c₁,g,g1),r) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,g,g1),r) is set
(c₁) . K23((c₁,g,g1),r) is set
(c₁,r,(c₁,g,g1)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (r,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁,g,g1),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (r,c₁,c₁)),(modetrans ((c₁,g,g1),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,r,g) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (r,c₁,c₁)),(modetrans (g,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,r,g),g1) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,r,g),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,r,g),c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁) . (g1,(c₁,r,g)) is Element of BoundedLinearOperators (c₁,c₁)
K23(g1,(c₁,r,g)) is set
(c₁) . K23(g1,(c₁,r,g)) is set
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
1. (c₁) is Element of the carrier of (c₁)
the OneF of (c₁) is Element of the carrier of (c₁)
RBLOP * (1. (c₁)) is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (RBLOP,(1. (c₁))) is Element of the carrier of (c₁)
K23(RBLOP,(1. (c₁))) is set
the multF of (c₁) . K23(RBLOP,(1. (c₁))) is set
seq is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁),seq) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (seq,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (seq,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
seq is Element of the carrier of (c₁)
seq1 is Element of the carrier of (c₁)
seq + seq1 is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (seq,seq1) is Element of the carrier of (c₁)
K23(seq,seq1) is set
the addF of (c₁) . K23(seq,seq1) is set
RBLOP * (seq + seq1) is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . (RBLOP,(seq + seq1)) is Element of the carrier of (c₁)
K23(RBLOP,(seq + seq1)) is set
the multF of (c₁) . K23(RBLOP,(seq + seq1)) is set
RBLOP * seq is Element of the carrier of (c₁)
the multF of (c₁) . (RBLOP,seq) is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the multF of (c₁) . K23(RBLOP,seq) is set
RBLOP * seq1 is Element of the carrier of (c₁)
the multF of (c₁) . (RBLOP,seq1) is Element of the carrier of (c₁)
K23(RBLOP,seq1) is set
the multF of (c₁) . K23(RBLOP,seq1) is set
(RBLOP * seq) + (RBLOP * seq1) is Element of the carrier of (c₁)
the addF of (c₁) . ((RBLOP * seq),(RBLOP * seq1)) is Element of the carrier of (c₁)
K23((RBLOP * seq),(RBLOP * seq1)) is set
the addF of (c₁) . K23((RBLOP * seq),(RBLOP * seq1)) is set
g is Element of BoundedLinearOperators (c₁,c₁)
r is Element of BoundedLinearOperators (c₁,c₁)
(c₁,g,r) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (g,r) is Element of BoundedLinearOperators (c₁,c₁)
K23(g,r) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(g,r) is set
g1 is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁,g,r),g1) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,g,r),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (g1,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,g,r),c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,g,g1) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (g,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,r,g1) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (r,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (r,c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,g,g1),(c₁,r,g1)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,g,g1),(c₁,r,g1)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,g,g1),(c₁,r,g1)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,g,g1),(c₁,r,g1)) is set
(c₁) . (g1,r) is Element of BoundedLinearOperators (c₁,c₁)
K23(g1,r) is set
(c₁) . K23(g1,r) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,g,g1),((c₁) . (g1,r))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,g,g1),((c₁) . (g1,r))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,g,g1),((c₁) . (g1,r))) is set
the carrier of (c₁) is non empty set
RBLOP is complex set
seq is Element of the carrier of (c₁)
seq1 is Element of the carrier of (c₁)
seq + seq1 is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (seq,seq1) is Element of the carrier of (c₁)
K23(seq,seq1) is set
the addF of (c₁) . K23(seq,seq1) is set
RBLOP * (seq + seq1) is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(RBLOP,(seq + seq1)) is set
the Mult of (c₁) . K23(RBLOP,(seq + seq1)) is set
RBLOP * seq is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the Mult of (c₁) . K23(RBLOP,seq) is set
RBLOP * seq1 is Element of the carrier of (c₁)
K23(RBLOP,seq1) is set
the Mult of (c₁) . K23(RBLOP,seq1) is set
(RBLOP * seq) + (RBLOP * seq1) is Element of the carrier of (c₁)
the addF of (c₁) . ((RBLOP * seq),(RBLOP * seq1)) is Element of the carrier of (c₁)
K23((RBLOP * seq),(RBLOP * seq1)) is set
the addF of (c₁) . K23((RBLOP * seq),(RBLOP * seq1)) is set
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
g1 + g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (g1,g) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(g1,g) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(g1,g) is set
RBLOP * (g1 + g) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
K23(RBLOP,(g1 + g)) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(RBLOP,(g1 + g)) is set
RBLOP * g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(RBLOP,g1) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(RBLOP,g1) is set
RBLOP * g is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(RBLOP,g) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(RBLOP,g) is set
(RBLOP * g1) + (RBLOP * g) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((RBLOP * g1),(RBLOP * g)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((RBLOP * g1),(RBLOP * g)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((RBLOP * g1),(RBLOP * g)) is set
the carrier of (c₁) is non empty set
RBLOP is complex set
seq is complex set
RBLOP + seq is complex set
seq1 is Element of the carrier of (c₁)
(RBLOP + seq) * seq1 is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23((RBLOP + seq),seq1) is set
the Mult of (c₁) . K23((RBLOP + seq),seq1) is set
RBLOP * seq1 is Element of the carrier of (c₁)
K23(RBLOP,seq1) is set
the Mult of (c₁) . K23(RBLOP,seq1) is set
seq * seq1 is Element of the carrier of (c₁)
K23(seq,seq1) is set
the Mult of (c₁) . K23(seq,seq1) is set
(RBLOP * seq1) + (seq * seq1) is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . ((RBLOP * seq1),(seq * seq1)) is Element of the carrier of (c₁)
K23((RBLOP * seq1),(seq * seq1)) is set
the addF of (c₁) . K23((RBLOP * seq1),(seq * seq1)) is set
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
(RBLOP + seq) * g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
K23((RBLOP + seq),g1) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((RBLOP + seq),g1) is set
RBLOP * g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(RBLOP,g1) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(RBLOP,g1) is set
seq * g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(seq,g1) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(seq,g1) is set
(RBLOP * g1) + (seq * g1) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((RBLOP * g1),(seq * g1)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((RBLOP * g1),(seq * g1)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((RBLOP * g1),(seq * g1)) is set
the carrier of (c₁) is non empty set
RBLOP is complex set
seq is complex set
RBLOP * seq is complex set
seq1 is Element of the carrier of (c₁)
(RBLOP * seq) * seq1 is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23((RBLOP * seq),seq1) is set
the Mult of (c₁) . K23((RBLOP * seq),seq1) is set
seq * seq1 is Element of the carrier of (c₁)
K23(seq,seq1) is set
the Mult of (c₁) . K23(seq,seq1) is set
RBLOP * (seq * seq1) is Element of the carrier of (c₁)
K23(RBLOP,(seq * seq1)) is set
the Mult of (c₁) . K23(RBLOP,(seq * seq1)) is set
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
(RBLOP * seq) * g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
K23((RBLOP * seq),g1) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((RBLOP * seq),g1) is set
seq * g1 is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(seq,g1) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(seq,g1) is set
RBLOP * (seq * g1) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(RBLOP,(seq * g1)) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(RBLOP,(seq * g1)) is set
the carrier of (c₁) is non empty set
RBLOP is Element of the carrier of (c₁)
seq is Element of the carrier of (c₁)
RBLOP * seq is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (RBLOP,seq) is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the multF of (c₁) . K23(RBLOP,seq) is set
seq1 is complex Element of COMPLEX
seq1 * (RBLOP * seq) is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(seq1,(RBLOP * seq)) is set
the Mult of (c₁) . K23(seq1,(RBLOP * seq)) is set
seq1 * RBLOP is Element of the carrier of (c₁)
K23(seq1,RBLOP) is set
the Mult of (c₁) . K23(seq1,RBLOP) is set
(seq1 * RBLOP) * seq is Element of the carrier of (c₁)
the multF of (c₁) . ((seq1 * RBLOP),seq) is Element of the carrier of (c₁)
K23((seq1 * RBLOP),seq) is set
the multF of (c₁) . K23((seq1 * RBLOP),seq) is set
g is Element of BoundedLinearOperators (c₁,c₁)
g1 is Element of BoundedLinearOperators (c₁,c₁)
(c₁,g,g1) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (g,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (g1,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,g,g1),seq1) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (seq1,(c₁,g,g1)) is set
K23(seq1,(c₁,g,g1)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(seq1,(c₁,g,g1)) is set
(c₁,g1,seq1) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (seq1,g1) is set
K23(seq1,g1) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(seq1,g1) is set
(c₁,g,(c₁,g1,seq1)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,g1,seq1),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans ((c₁,g1,seq1),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative unital associative right-distributive right_unital strict vector-associative ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
c₁ is non empty V13() V16( NAT ) V17( the carrier of Complex_l1_Space) Function-like V23( NAT ) V27( NAT , the carrier of Complex_l1_Space) Element of bool [:NAT, the carrier of Complex_l1_Space:]
2 is non empty epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real positive non negative V57() V58() V59() V60() V61() V62() Element of NAT
1 / 2 is non empty complex real ext-real positive non negative Element of COMPLEX
<i> is complex Element of COMPLEX
0 * <i> is complex set
(1 / 2) + (0 * <i>) is complex set
c₁ is complex Element of COMPLEX
c₁ GeoSeq is non empty V13() V16( NAT ) V17( COMPLEX ) Function-like V23( NAT ) V27( NAT , COMPLEX ) V35() Element of bool [:NAT,COMPLEX:]
NRM is non empty V13() V16( NAT ) V17( COMPLEX ) Function-like V23( NAT ) V27( NAT , COMPLEX ) V35() Element of bool [:NAT,COMPLEX:]
|.NRM.| is non empty V13() V16( NAT ) V17( REAL ) Function-like V23( NAT ) V27( NAT , REAL ) V35() V36() V37() Element of bool [:NAT,REAL:]
|.c₁.| is complex real ext-real Element of REAL
UNIT is epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real V57() V58() V59() V60() V61() V62() Element of NAT
UNIT + 1 is complex real ext-real Element of REAL
|.NRM.| . (UNIT + 1) is complex real ext-real set
|.NRM.| . UNIT is complex real ext-real Element of REAL
(|.NRM.| . UNIT) * |.c₁.| is complex real ext-real Element of REAL
NRM . (UNIT + 1) is complex set
|.(NRM . (UNIT + 1)).| is complex real ext-real Element of REAL
NRM . UNIT is complex Element of COMPLEX
(NRM . UNIT) * c₁ is complex Element of COMPLEX
|.((NRM . UNIT) * c₁).| is complex real ext-real Element of REAL
|.(NRM . UNIT).| is complex real ext-real Element of REAL
|.(NRM . UNIT).| * |.c₁.| is complex real ext-real Element of REAL
|.NRM.| . 0 is complex real ext-real Element of REAL
NRM . 0 is complex Element of COMPLEX
|.(NRM . 0).| is complex real ext-real Element of REAL
|.c₁.| GeoSeq is non empty V13() V16( NAT ) V17( REAL ) Function-like V23( NAT ) V27( NAT , REAL ) V35() V36() V37() Element of bool [:NAT,REAL:]
seq_id NRM is non empty V13() V16( NAT ) V17( COMPLEX ) Function-like V23( NAT ) V27( NAT , COMPLEX ) V35() Element of bool [:NAT,COMPLEX:]
UNIT is right_complementable Element of the carrier of Complex_l1_Space
seq_id UNIT is non empty V13() V16( NAT ) V17( COMPLEX ) Function-like V23( NAT ) V27( NAT , COMPLEX ) V35() Element of bool [:NAT,COMPLEX:]
(seq_id UNIT) . 0 is complex Element of COMPLEX
c₁ is non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
the carrier of c₁ is non empty non trivial set
0. c₁ is zero right_complementable Element of the carrier of c₁
the ZeroF of c₁ is right_complementable Element of the carrier of c₁
NRM is right_complementable Element of the carrier of c₁
||.NRM.|| is complex real ext-real Element of REAL
the normF of c₁ is non empty V13() V16( the carrier of c₁) V17( REAL ) Function-like V23( the carrier of c₁) V27( the carrier of c₁, REAL ) V35() V36() V37() Element of bool [: the carrier of c₁,REAL:]
[: the carrier of c₁,REAL:] is V35() V36() V37() set
bool [: the carrier of c₁,REAL:] is set
the normF of c₁ . NRM is complex real ext-real Element of REAL
<i> is complex Element of COMPLEX
0 * <i> is complex set
||.NRM.|| + (0 * <i>) is complex set
UNIT is complex Element of COMPLEX
UNIT " is complex Element of COMPLEX
(UNIT ") * NRM is right_complementable Element of the carrier of c₁
the Mult of c₁ is V13() V16([:COMPLEX, the carrier of c₁:]) V17( the carrier of c₁) Function-like V23([:COMPLEX, the carrier of c₁:]) V27([:COMPLEX, the carrier of c₁:], the carrier of c₁) Element of bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:]
[:COMPLEX, the carrier of c₁:] is set
[:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
bool [:[:COMPLEX, the carrier of c₁:], the carrier of c₁:] is set
K23((UNIT "),NRM) is set
the Mult of c₁ . K23((UNIT "),NRM) is set
MULT is right_complementable Element of the carrier of c₁
||.MULT.|| is complex real ext-real Element of REAL
the normF of c₁ . MULT is complex real ext-real Element of REAL
|.(UNIT ").| is complex real ext-real Element of REAL
1r * (UNIT ") is complex Element of COMPLEX
|.(1r * (UNIT ")).| is complex real ext-real Element of REAL
1r / UNIT is complex Element of COMPLEX
|.(1r / UNIT).| is complex real ext-real Element of REAL
|.UNIT.| is complex real ext-real Element of REAL
1 / |.UNIT.| is complex real ext-real Element of COMPLEX
|.UNIT.| " is complex real ext-real Element of REAL
1 * (|.UNIT.| ") is complex real ext-real Element of REAL
||.NRM.|| " is complex real ext-real Element of REAL
|.(UNIT ").| * ||.NRM.|| is complex real ext-real Element of REAL
c₁ is non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty non trivial set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
(BoundedLinearOperatorsNorm (c₁,c₁)) . (id the carrier of c₁) is complex real ext-real set
NRM is right_complementable Element of the carrier of c₁
||.NRM.|| is complex real ext-real Element of REAL
the normF of c₁ is non empty V13() V16( the carrier of c₁) V17( REAL ) Function-like V23( the carrier of c₁) V27( the carrier of c₁, REAL ) V35() V36() V37() Element of bool [: the carrier of c₁,REAL:]
[: the carrier of c₁,REAL:] is V35() V36() V37() set
bool [: the carrier of c₁,REAL:] is set
the normF of c₁ . NRM is complex real ext-real Element of REAL
MULT is complex real ext-real Element of REAL
UNIT is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
PreNorms UNIT is non empty V57() V58() V59() Element of bool REAL
{ ||.(UNIT . b₁).|| where b₁ is right_complementable Element of the carrier of c₁ : ||.b₁.|| <= 1 } is set
ADD is right_complementable Element of the carrier of c₁
UNIT . ADD is right_complementable Element of the carrier of c₁
||.(UNIT . ADD).|| is complex real ext-real Element of REAL
the normF of c₁ . (UNIT . ADD) is complex real ext-real Element of REAL
||.ADD.|| is complex real ext-real Element of REAL
the normF of c₁ . ADD is complex real ext-real Element of REAL
UNIT . NRM is right_complementable Element of the carrier of c₁
upper_bound (PreNorms UNIT) is complex real ext-real Element of REAL
MULT is complex real ext-real set
the non empty set is non empty set
[: the non empty set , the non empty set :] is set
[:[: the non empty set , the non empty set :], the non empty set :] is set
bool [:[: the non empty set , the non empty set :], the non empty set :] is set
the V13() V16([: the non empty set , the non empty set :]) V17( the non empty set ) Function-like V23([: the non empty set , the non empty set :]) V27([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :] is V13() V16([: the non empty set , the non empty set :]) V17( the non empty set ) Function-like V23([: the non empty set , the non empty set :]) V27([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :]
[:COMPLEX, the non empty set :] is set
[:[:COMPLEX, the non empty set :], the non empty set :] is set
bool [:[:COMPLEX, the non empty set :], the non empty set :] is set
the V13() V16([:COMPLEX, the non empty set :]) V17( the non empty set ) Function-like V23([:COMPLEX, the non empty set :]) V27([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :] is V13() V16([:COMPLEX, the non empty set :]) V17( the non empty set ) Function-like V23([:COMPLEX, the non empty set :]) V27([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :]
the Element of the non empty set is Element of the non empty set
[: the non empty set ,REAL:] is V35() V36() V37() set
bool [: the non empty set ,REAL:] is set
the non empty V13() V16( the non empty set ) V17( REAL ) Function-like V23( the non empty set ) V27( the non empty set , REAL ) V35() V36() V37() Element of bool [: the non empty set ,REAL:] is non empty V13() V16( the non empty set ) V17( REAL ) Function-like V23( the non empty set ) V27( the non empty set , REAL ) V35() V36() V37() Element of bool [: the non empty set ,REAL:]
( the non empty set , the V13() V16([: the non empty set , the non empty set :]) V17( the non empty set ) Function-like V23([: the non empty set , the non empty set :]) V27([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :], the V13() V16([: the non empty set , the non empty set :]) V17( the non empty set ) Function-like V23([: the non empty set , the non empty set :]) V27([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :], the V13() V16([:COMPLEX, the non empty set :]) V17( the non empty set ) Function-like V23([:COMPLEX, the non empty set :]) V27([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :], the Element of the non empty set , the Element of the non empty set , the non empty V13() V16( the non empty set ) V17( REAL ) Function-like V23( the non empty set ) V27( the non empty set , REAL ) V35() V36() V37() Element of bool [: the non empty set ,REAL:]) is () ()
the carrier of ( the non empty set , the V13() V16([: the non empty set , the non empty set :]) V17( the non empty set ) Function-like V23([: the non empty set , the non empty set :]) V27([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :], the V13() V16([: the non empty set , the non empty set :]) V17( the non empty set ) Function-like V23([: the non empty set , the non empty set :]) V27([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :], the V13() V16([:COMPLEX, the non empty set :]) V17( the non empty set ) Function-like V23([:COMPLEX, the non empty set :]) V27([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :], the Element of the non empty set , the Element of the non empty set , the non empty V13() V16( the non empty set ) V17( REAL ) Function-like V23( the non empty set ) V27( the non empty set , REAL ) V35() V36() V37() Element of bool [: the non empty set ,REAL:]) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
the carrier of (c₁) is non empty set
UNIT is Element of the carrier of (c₁)
MULT is Element of the carrier of (c₁)
UNIT * MULT is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
K23(UNIT,MULT) is set
the multF of (c₁) . K23(UNIT,MULT) is set
ADD is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(c₁),ADD) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (ADD,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (ADD,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
MULT * UNIT is Element of the carrier of (c₁)
the multF of (c₁) . (MULT,UNIT) is Element of the carrier of (c₁)
K23(MULT,UNIT) is set
the multF of (c₁) . K23(MULT,UNIT) is set
(c₁,ADD,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (ADD,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
the carrier of (c₁) is non empty set
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
UNIT * NRM is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the multF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
NRM * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,MULT) is Element of the carrier of (c₁)
K23(NRM,MULT) is set
the multF of (c₁) . K23(NRM,MULT) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty unital () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
the carrier of (c₁) is non empty set
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
1. (c₁) is Element of the carrier of (c₁)
the OneF of (c₁) is Element of the carrier of (c₁)
NRM is Element of the carrier of (c₁)
UNIT is Element of the carrier of (c₁)
NRM + UNIT is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
K23(NRM,UNIT) is set
the addF of (c₁) . K23(NRM,UNIT) is set
UNIT + NRM is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
K23(UNIT,NRM) is set
the addF of (c₁) . K23(UNIT,NRM) is set
MULT is Element of the carrier of (c₁)
(NRM + UNIT) + MULT is Element of the carrier of (c₁)
the addF of (c₁) . ((NRM + UNIT),MULT) is Element of the carrier of (c₁)
K23((NRM + UNIT),MULT) is set
the addF of (c₁) . K23((NRM + UNIT),MULT) is set
UNIT + MULT is Element of the carrier of (c₁)
the addF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
K23(UNIT,MULT) is set
the addF of (c₁) . K23(UNIT,MULT) is set
NRM + (UNIT + MULT) is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,(UNIT + MULT)) is Element of the carrier of (c₁)
K23(NRM,(UNIT + MULT)) is set
the addF of (c₁) . K23(NRM,(UNIT + MULT)) is set
NRM + (0. (c₁)) is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,(0. (c₁))) is Element of the carrier of (c₁)
K23(NRM,(0. (c₁))) is set
the addF of (c₁) . K23(NRM,(0. (c₁))) is set
NRM * UNIT is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . (NRM,UNIT) is Element of the carrier of (c₁)
the multF of (c₁) . K23(NRM,UNIT) is set
(NRM * UNIT) * MULT is Element of the carrier of (c₁)
the multF of (c₁) . ((NRM * UNIT),MULT) is Element of the carrier of (c₁)
K23((NRM * UNIT),MULT) is set
the multF of (c₁) . K23((NRM * UNIT),MULT) is set
UNIT * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (UNIT,MULT) is Element of the carrier of (c₁)
the multF of (c₁) . K23(UNIT,MULT) is set
NRM * (UNIT * MULT) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(UNIT * MULT)) is Element of the carrier of (c₁)
K23(NRM,(UNIT * MULT)) is set
the multF of (c₁) . K23(NRM,(UNIT * MULT)) is set
NRM * (1. (c₁)) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(1. (c₁))) is Element of the carrier of (c₁)
K23(NRM,(1. (c₁))) is set
the multF of (c₁) . K23(NRM,(1. (c₁))) is set
(1. (c₁)) * NRM is Element of the carrier of (c₁)
the multF of (c₁) . ((1. (c₁)),NRM) is Element of the carrier of (c₁)
K23((1. (c₁)),NRM) is set
the multF of (c₁) . K23((1. (c₁)),NRM) is set
NRM * (UNIT + MULT) is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,(UNIT + MULT)) is Element of the carrier of (c₁)
the multF of (c₁) . K23(NRM,(UNIT + MULT)) is set
NRM * MULT is Element of the carrier of (c₁)
the multF of (c₁) . (NRM,MULT) is Element of the carrier of (c₁)
K23(NRM,MULT) is set
the multF of (c₁) . K23(NRM,MULT) is set
(NRM * UNIT) + (NRM * MULT) is Element of the carrier of (c₁)
the addF of (c₁) . ((NRM * UNIT),(NRM * MULT)) is Element of the carrier of (c₁)
K23((NRM * UNIT),(NRM * MULT)) is set
the addF of (c₁) . K23((NRM * UNIT),(NRM * MULT)) is set
(UNIT + MULT) * NRM is Element of the carrier of (c₁)
the multF of (c₁) . ((UNIT + MULT),NRM) is Element of the carrier of (c₁)
K23((UNIT + MULT),NRM) is set
the multF of (c₁) . K23((UNIT + MULT),NRM) is set
UNIT * NRM is Element of the carrier of (c₁)
the multF of (c₁) . (UNIT,NRM) is Element of the carrier of (c₁)
the multF of (c₁) . K23(UNIT,NRM) is set
MULT * NRM is Element of the carrier of (c₁)
the multF of (c₁) . (MULT,NRM) is Element of the carrier of (c₁)
K23(MULT,NRM) is set
the multF of (c₁) . K23(MULT,NRM) is set
(UNIT * NRM) + (MULT * NRM) is Element of the carrier of (c₁)
the addF of (c₁) . ((UNIT * NRM),(MULT * NRM)) is Element of the carrier of (c₁)
K23((UNIT * NRM),(MULT * NRM)) is set
the addF of (c₁) . K23((UNIT * NRM),(MULT * NRM)) is set
1r * NRM is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(1r,NRM) is set
the Mult of (c₁) . K23(1r,NRM) is set
ADD is complex set
ADD * (NRM * UNIT) is Element of the carrier of (c₁)
K23(ADD,(NRM * UNIT)) is set
the Mult of (c₁) . K23(ADD,(NRM * UNIT)) is set
ADD * NRM is Element of the carrier of (c₁)
K23(ADD,NRM) is set
the Mult of (c₁) . K23(ADD,NRM) is set
(ADD * NRM) * UNIT is Element of the carrier of (c₁)
the multF of (c₁) . ((ADD * NRM),UNIT) is Element of the carrier of (c₁)
K23((ADD * NRM),UNIT) is set
the multF of (c₁) . K23((ADD * NRM),UNIT) is set
BS is complex set
ADD * BS is complex set
(ADD * BS) * (NRM * UNIT) is Element of the carrier of (c₁)
K23((ADD * BS),(NRM * UNIT)) is set
the Mult of (c₁) . K23((ADD * BS),(NRM * UNIT)) is set
BS * UNIT is Element of the carrier of (c₁)
K23(BS,UNIT) is set
the Mult of (c₁) . K23(BS,UNIT) is set
(ADD * NRM) * (BS * UNIT) is Element of the carrier of (c₁)
the multF of (c₁) . ((ADD * NRM),(BS * UNIT)) is Element of the carrier of (c₁)
K23((ADD * NRM),(BS * UNIT)) is set
the multF of (c₁) . K23((ADD * NRM),(BS * UNIT)) is set
ADD * (NRM + UNIT) is Element of the carrier of (c₁)
K23(ADD,(NRM + UNIT)) is set
the Mult of (c₁) . K23(ADD,(NRM + UNIT)) is set
ADD * UNIT is Element of the carrier of (c₁)
K23(ADD,UNIT) is set
the Mult of (c₁) . K23(ADD,UNIT) is set
(ADD * NRM) + (ADD * UNIT) is Element of the carrier of (c₁)
the addF of (c₁) . ((ADD * NRM),(ADD * UNIT)) is Element of the carrier of (c₁)
K23((ADD * NRM),(ADD * UNIT)) is set
the addF of (c₁) . K23((ADD * NRM),(ADD * UNIT)) is set
ADD + BS is complex set
(ADD + BS) * NRM is Element of the carrier of (c₁)
K23((ADD + BS),NRM) is set
the Mult of (c₁) . K23((ADD + BS),NRM) is set
BS * NRM is Element of the carrier of (c₁)
K23(BS,NRM) is set
the Mult of (c₁) . K23(BS,NRM) is set
(ADD * NRM) + (BS * NRM) is Element of the carrier of (c₁)
the addF of (c₁) . ((ADD * NRM),(BS * NRM)) is Element of the carrier of (c₁)
K23((ADD * NRM),(BS * NRM)) is set
the addF of (c₁) . K23((ADD * NRM),(BS * NRM)) is set
(ADD * BS) * NRM is Element of the carrier of (c₁)
K23((ADD * BS),NRM) is set
the Mult of (c₁) . K23((ADD * BS),NRM) is set
ADD * (BS * NRM) is Element of the carrier of (c₁)
K23(ADD,(BS * NRM)) is set
the Mult of (c₁) . K23(ADD,(BS * NRM)) is set
CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty set
r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
r + m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[: the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #), the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,m) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,m) is set
n is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
(r + m) + n is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((r + m),n) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((r + m),n) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((r + m),n) is set
m + n is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (m,n) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(m,n) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(m,n) is set
r + (m + n) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,(m + n)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,(m + n)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,(m + n)) is set
0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is zero right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the ZeroF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
r + (0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,(0. CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #))) is set
xx is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
r + xx is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . (r,xx) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(r,xx) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(r,xx) is set
yy is Element of the carrier of (c₁)
NRM + yy is Element of the carrier of (c₁)
the addF of (c₁) . (NRM,yy) is Element of the carrier of (c₁)
K23(NRM,yy) is set
the addF of (c₁) . K23(NRM,yy) is set
yy is Element of BoundedLinearOperators (c₁,c₁)
xx is Element of BoundedLinearOperators (c₁,c₁)
(c₁,yy,xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (yy,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans (xx,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (yy,c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
zz is Element of BoundedLinearOperators (c₁,c₁)
(c₁) . ((c₁,yy,xx),zz) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,yy,xx),zz) is set
(c₁) . K23((c₁,yy,xx),zz) is set
(c₁,zz,(c₁,yy,xx)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (zz,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁,yy,xx),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (zz,c₁,c₁)),(modetrans ((c₁,yy,xx),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,zz,yy) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (zz,c₁,c₁)),(modetrans (yy,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,zz,yy),xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,zz,yy),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,zz,yy),c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁) . (xx,(c₁,zz,yy)) is Element of BoundedLinearOperators (c₁,c₁)
K23(xx,(c₁,zz,yy)) is set
(c₁) . K23(xx,(c₁,zz,yy)) is set
(c₁,(c₁),xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁),c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,yy,zz) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (yy,zz) is Element of BoundedLinearOperators (c₁,c₁)
K23(yy,zz) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(yy,zz) is set
(c₁,(c₁,yy,zz),xx) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,yy,zz),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,yy,zz),c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,zz,xx) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (zz,c₁,c₁)),(modetrans (xx,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,yy,xx),(c₁,zz,xx)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,yy,xx),(c₁,zz,xx)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,yy,xx),(c₁,zz,xx)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,yy,xx),(c₁,zz,xx)) is set
(c₁) . (xx,zz) is Element of BoundedLinearOperators (c₁,c₁)
K23(xx,zz) is set
(c₁) . K23(xx,zz) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,yy,xx),((c₁) . (xx,zz))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,yy,xx),((c₁) . (xx,zz))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,yy,xx),((c₁) . (xx,zz))) is set
(c₁,xx,(c₁,yy,zz)) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans ((c₁,yy,zz),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,yy) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans (yy,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,xx,zz) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (xx,c₁,c₁)),(modetrans (zz,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,xx,yy),(c₁,xx,zz)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,xx,yy),(c₁,xx,zz)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,xx,yy),(c₁,xx,zz)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,xx,yy),(c₁,xx,zz)) is set
(c₁) . (zz,xx) is Element of BoundedLinearOperators (c₁,c₁)
K23(zz,xx) is set
(c₁) . K23(zz,xx) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,xx,yy),((c₁) . (zz,xx))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,xx,yy),((c₁) . (zz,xx))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,xx,yy),((c₁) . (zz,xx))) is set
(c₁,(c₁,yy,xx),ADD) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (ADD,(c₁,yy,xx)) is set
K23(ADD,(c₁,yy,xx)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(ADD,(c₁,yy,xx)) is set
(c₁,xx,ADD) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (ADD,xx) is set
K23(ADD,xx) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(ADD,xx) is set
(c₁,yy,(c₁,xx,ADD)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,xx,ADD),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (yy,c₁,c₁)),(modetrans ((c₁,xx,ADD),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,yy,xx),(ADD * BS)) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((ADD * BS),(c₁,yy,xx)) is set
K23((ADD * BS),(c₁,yy,xx)) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((ADD * BS),(c₁,yy,xx)) is set
(c₁,yy,BS) is Element of BoundedLinearOperators (c₁,c₁)
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (BS,yy) is set
K23(BS,yy) is set
(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(BS,yy) is set
(c₁,(c₁,yy,BS),(c₁,xx,ADD)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans ((c₁,yy,BS),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans ((c₁,yy,BS),c₁,c₁)),(modetrans ((c₁,xx,ADD),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
ADD * (r + m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is V13() V16([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V17( the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Function-like V23([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]) V27([:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)) Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):]
[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
[:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
bool [:[:COMPLEX, the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):], the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #):] is set
K23(ADD,(r + m)) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,(r + m)) is set
ADD * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(ADD,r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,r) is set
ADD * m is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(ADD,m) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,m) is set
(ADD * r) + (ADD * m) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((ADD * r),(ADD * m)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD * r),(ADD * m)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD * r),(ADD * m)) is set
(ADD + BS) * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD + BS),r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD + BS),r) is set
BS * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(BS,r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(BS,r) is set
(ADD * r) + (BS * r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . ((ADD * r),(BS * r)) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD * r),(BS * r)) is set
the addF of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD * r),(BS * r)) is set
(ADD * BS) * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23((ADD * BS),r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23((ADD * BS),r) is set
ADD * (BS * r) is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(ADD,(BS * r)) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(ADD,(BS * r)) is set
1r * r is right_complementable Element of the carrier of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #)
K23(1r,r) is set
the Mult of CLSStruct(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) . K23(1r,r) is set
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty unital () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
C_NormSpace_of_BoundedLinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
CNORMSTR(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁)) #) is non empty strict CNORMSTR
0. (c₁) is zero Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
the ZeroF of (c₁) is Element of the carrier of (c₁)
||.(0. (c₁)).|| is complex real ext-real Element of REAL
the normF of (c₁) is non empty V13() V16( the carrier of (c₁)) V17( REAL ) Function-like V23( the carrier of (c₁)) V27( the carrier of (c₁), REAL ) V35() V36() V37() Element of bool [: the carrier of (c₁),REAL:]
[: the carrier of (c₁),REAL:] is V35() V36() V37() set
bool [: the carrier of (c₁),REAL:] is set
the normF of (c₁) . (0. (c₁)) is complex real ext-real Element of REAL
0. (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() Function-like zero right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
the ZeroF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
||.(0. (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))).|| is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real Function-like functional ext-real non positive non negative V57() V58() V59() V60() V61() V62() V63() Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty V13() V16( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V17( REAL ) Function-like V23( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V27( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), REAL ) V35() V36() V37() Element of bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is set
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (0. (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) is complex real ext-real Element of REAL
the carrier of (c₁) is non empty set
MULT is Element of the carrier of (c₁)
||.MULT.|| is complex real ext-real Element of REAL
the normF of (c₁) is non empty V13() V16( the carrier of (c₁)) V17( REAL ) Function-like V23( the carrier of (c₁)) V27( the carrier of (c₁), REAL ) V35() V36() V37() Element of bool [: the carrier of (c₁),REAL:]
[: the carrier of (c₁),REAL:] is V35() V36() V37() set
bool [: the carrier of (c₁),REAL:] is set
the normF of (c₁) . MULT is complex real ext-real Element of REAL
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
ADD is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
||.ADD.|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty V13() V16( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V17( REAL ) Function-like V23( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V27( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), REAL ) V35() V36() V37() Element of bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is set
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . ADD is complex real ext-real Element of REAL
0. (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() Function-like zero right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the ZeroF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the carrier of (c₁) is non empty set
MULT is Element of the carrier of (c₁)
||.MULT.|| is complex real ext-real Element of REAL
the normF of (c₁) is non empty V13() V16( the carrier of (c₁)) V17( REAL ) Function-like V23( the carrier of (c₁)) V27( the carrier of (c₁), REAL ) V35() V36() V37() Element of bool [: the carrier of (c₁),REAL:]
[: the carrier of (c₁),REAL:] is V35() V36() V37() set
bool [: the carrier of (c₁),REAL:] is set
the normF of (c₁) . MULT is complex real ext-real Element of REAL
ADD is Element of the carrier of (c₁)
MULT + ADD is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (MULT,ADD) is Element of the carrier of (c₁)
K23(MULT,ADD) is set
the addF of (c₁) . K23(MULT,ADD) is set
||.(MULT + ADD).|| is complex real ext-real Element of REAL
the normF of (c₁) . (MULT + ADD) is complex real ext-real Element of REAL
||.ADD.|| is complex real ext-real Element of REAL
the normF of (c₁) . ADD is complex real ext-real Element of REAL
||.MULT.|| + ||.ADD.|| is complex real ext-real Element of REAL
BS is complex set
BS * MULT is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(BS,MULT) is set
the Mult of (c₁) . K23(BS,MULT) is set
||.(BS * MULT).|| is complex real ext-real Element of REAL
the normF of (c₁) . (BS * MULT) is complex real ext-real Element of REAL
|.BS.| is complex real ext-real Element of REAL
|.BS.| * ||.MULT.|| is complex real ext-real Element of REAL
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
BLOP is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
||.BLOP.|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty V13() V16( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V17( REAL ) Function-like V23( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V27( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), REAL ) V35() V36() V37() Element of bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is set
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . BLOP is complex real ext-real Element of REAL
BS * BLOP is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
K23(BS,BLOP) is set
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(BS,BLOP) is set
||.(BS * BLOP).|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (BS * BLOP) is complex real ext-real Element of REAL
RBLOP is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
BLOP + RBLOP is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (BLOP,RBLOP) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23(BLOP,RBLOP) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23(BLOP,RBLOP) is set
||.(BLOP + RBLOP).|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . (BLOP + RBLOP) is complex real ext-real Element of REAL
||.RBLOP.|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . RBLOP is complex real ext-real Element of REAL
||.BLOP.|| + ||.RBLOP.|| is complex real ext-real Element of REAL
the carrier of (c₁) is non empty set
ADD is Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
BLOP is Element of the carrier of (c₁)
ADD is complex set
BS is complex set
ADD + BS is complex set
(ADD + BS) * BLOP is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23((ADD + BS),BLOP) is set
the Mult of (c₁) . K23((ADD + BS),BLOP) is set
ADD * BLOP is Element of the carrier of (c₁)
K23(ADD,BLOP) is set
the Mult of (c₁) . K23(ADD,BLOP) is set
BS * BLOP is Element of the carrier of (c₁)
K23(BS,BLOP) is set
the Mult of (c₁) . K23(BS,BLOP) is set
(ADD * BLOP) + (BS * BLOP) is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . ((ADD * BLOP),(BS * BLOP)) is Element of the carrier of (c₁)
K23((ADD * BLOP),(BS * BLOP)) is set
the addF of (c₁) . K23((ADD * BLOP),(BS * BLOP)) is set
seq1 is Element of the carrier of (c₁)
RBLOP is complex set
seq is complex set
RBLOP * seq is complex set
(RBLOP * seq) * seq1 is Element of the carrier of (c₁)
K23((RBLOP * seq),seq1) is set
the Mult of (c₁) . K23((RBLOP * seq),seq1) is set
seq * seq1 is Element of the carrier of (c₁)
K23(seq,seq1) is set
the Mult of (c₁) . K23(seq,seq1) is set
RBLOP * (seq * seq1) is Element of the carrier of (c₁)
K23(RBLOP,(seq * seq1)) is set
the Mult of (c₁) . K23(RBLOP,(seq * seq1)) is set
0. (c₁) is zero Element of the carrier of (c₁)
the ZeroF of (c₁) is Element of the carrier of (c₁)
1. (c₁) is Element of the carrier of (c₁)
the OneF of (c₁) is Element of the carrier of (c₁)
ADD is Element of the carrier of (c₁)
BS is Element of the carrier of (c₁)
ADD + BS is Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (ADD,BS) is Element of the carrier of (c₁)
K23(ADD,BS) is set
the addF of (c₁) . K23(ADD,BS) is set
BS + ADD is Element of the carrier of (c₁)
the addF of (c₁) . (BS,ADD) is Element of the carrier of (c₁)
K23(BS,ADD) is set
the addF of (c₁) . K23(BS,ADD) is set
BLOP is Element of the carrier of (c₁)
RBLOP is Element of the carrier of (c₁)
BLOP + RBLOP is Element of the carrier of (c₁)
the addF of (c₁) . (BLOP,RBLOP) is Element of the carrier of (c₁)
K23(BLOP,RBLOP) is set
the addF of (c₁) . K23(BLOP,RBLOP) is set
seq is Element of the carrier of (c₁)
(BLOP + RBLOP) + seq is Element of the carrier of (c₁)
the addF of (c₁) . ((BLOP + RBLOP),seq) is Element of the carrier of (c₁)
K23((BLOP + RBLOP),seq) is set
the addF of (c₁) . K23((BLOP + RBLOP),seq) is set
RBLOP + seq is Element of the carrier of (c₁)
the addF of (c₁) . (RBLOP,seq) is Element of the carrier of (c₁)
K23(RBLOP,seq) is set
the addF of (c₁) . K23(RBLOP,seq) is set
BLOP + (RBLOP + seq) is Element of the carrier of (c₁)
the addF of (c₁) . (BLOP,(RBLOP + seq)) is Element of the carrier of (c₁)
K23(BLOP,(RBLOP + seq)) is set
the addF of (c₁) . K23(BLOP,(RBLOP + seq)) is set
seq1 is Element of the carrier of (c₁)
seq1 + (0. (c₁)) is Element of the carrier of (c₁)
the addF of (c₁) . (seq1,(0. (c₁))) is Element of the carrier of (c₁)
K23(seq1,(0. (c₁))) is set
the addF of (c₁) . K23(seq1,(0. (c₁))) is set
g1 is Element of the carrier of (c₁)
g is Element of the carrier of (c₁)
r is Element of the carrier of (c₁)
g * r is Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . (g,r) is Element of the carrier of (c₁)
K23(g,r) is set
the multF of (c₁) . K23(g,r) is set
m is Element of the carrier of (c₁)
(g * r) * m is Element of the carrier of (c₁)
the multF of (c₁) . ((g * r),m) is Element of the carrier of (c₁)
K23((g * r),m) is set
the multF of (c₁) . K23((g * r),m) is set
r * m is Element of the carrier of (c₁)
the multF of (c₁) . (r,m) is Element of the carrier of (c₁)
K23(r,m) is set
the multF of (c₁) . K23(r,m) is set
g * (r * m) is Element of the carrier of (c₁)
the multF of (c₁) . (g,(r * m)) is Element of the carrier of (c₁)
K23(g,(r * m)) is set
the multF of (c₁) . K23(g,(r * m)) is set
n is Element of the carrier of (c₁)
n * (1. (c₁)) is Element of the carrier of (c₁)
the multF of (c₁) . (n,(1. (c₁))) is Element of the carrier of (c₁)
K23(n,(1. (c₁))) is set
the multF of (c₁) . K23(n,(1. (c₁))) is set
xx is Element of the carrier of (c₁)
(1. (c₁)) * xx is Element of the carrier of (c₁)
the multF of (c₁) . ((1. (c₁)),xx) is Element of the carrier of (c₁)
K23((1. (c₁)),xx) is set
the multF of (c₁) . K23((1. (c₁)),xx) is set
yy is Element of the carrier of (c₁)
zz is Element of the carrier of (c₁)
c₁₉ is Element of the carrier of (c₁)
zz + c₁₉ is Element of the carrier of (c₁)
the addF of (c₁) . (zz,c₁₉) is Element of the carrier of (c₁)
K23(zz,c₁₉) is set
the addF of (c₁) . K23(zz,c₁₉) is set
yy * (zz + c₁₉) is Element of the carrier of (c₁)
the multF of (c₁) . (yy,(zz + c₁₉)) is Element of the carrier of (c₁)
K23(yy,(zz + c₁₉)) is set
the multF of (c₁) . K23(yy,(zz + c₁₉)) is set
yy * zz is Element of the carrier of (c₁)
the multF of (c₁) . (yy,zz) is Element of the carrier of (c₁)
K23(yy,zz) is set
the multF of (c₁) . K23(yy,zz) is set
yy * c₁₉ is Element of the carrier of (c₁)
the multF of (c₁) . (yy,c₁₉) is Element of the carrier of (c₁)
K23(yy,c₁₉) is set
the multF of (c₁) . K23(yy,c₁₉) is set
(yy * zz) + (yy * c₁₉) is Element of the carrier of (c₁)
the addF of (c₁) . ((yy * zz),(yy * c₁₉)) is Element of the carrier of (c₁)
K23((yy * zz),(yy * c₁₉)) is set
the addF of (c₁) . K23((yy * zz),(yy * c₁₉)) is set
c₂₁ is Element of the carrier of (c₁)
c₂₂ is Element of the carrier of (c₁)
c₂₁ + c₂₂ is Element of the carrier of (c₁)
the addF of (c₁) . (c₂₁,c₂₂) is Element of the carrier of (c₁)
K23(c₂₁,c₂₂) is set
the addF of (c₁) . K23(c₂₁,c₂₂) is set
c₂₀ is Element of the carrier of (c₁)
(c₂₁ + c₂₂) * c₂₀ is Element of the carrier of (c₁)
the multF of (c₁) . ((c₂₁ + c₂₂),c₂₀) is Element of the carrier of (c₁)
K23((c₂₁ + c₂₂),c₂₀) is set
the multF of (c₁) . K23((c₂₁ + c₂₂),c₂₀) is set
c₂₁ * c₂₀ is Element of the carrier of (c₁)
the multF of (c₁) . (c₂₁,c₂₀) is Element of the carrier of (c₁)
K23(c₂₁,c₂₀) is set
the multF of (c₁) . K23(c₂₁,c₂₀) is set
c₂₂ * c₂₀ is Element of the carrier of (c₁)
the multF of (c₁) . (c₂₂,c₂₀) is Element of the carrier of (c₁)
K23(c₂₂,c₂₀) is set
the multF of (c₁) . K23(c₂₂,c₂₀) is set
(c₂₁ * c₂₀) + (c₂₂ * c₂₀) is Element of the carrier of (c₁)
the addF of (c₁) . ((c₂₁ * c₂₀),(c₂₂ * c₂₀)) is Element of the carrier of (c₁)
K23((c₂₁ * c₂₀),(c₂₂ * c₂₀)) is set
the addF of (c₁) . K23((c₂₁ * c₂₀),(c₂₂ * c₂₀)) is set
c₂₃ is Element of the carrier of (c₁)
c₂₄ is Element of the carrier of (c₁)
c₂₃ * c₂₄ is Element of the carrier of (c₁)
the multF of (c₁) . (c₂₃,c₂₄) is Element of the carrier of (c₁)
K23(c₂₃,c₂₄) is set
the multF of (c₁) . K23(c₂₃,c₂₄) is set
c₂₅ is complex Element of COMPLEX
c₂₅ * (c₂₃ * c₂₄) is Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(c₂₅,(c₂₃ * c₂₄)) is set
the Mult of (c₁) . K23(c₂₅,(c₂₃ * c₂₄)) is set
c₂₅ * c₂₃ is Element of the carrier of (c₁)
K23(c₂₅,c₂₃) is set
the Mult of (c₁) . K23(c₂₅,c₂₃) is set
(c₂₅ * c₂₃) * c₂₄ is Element of the carrier of (c₁)
the multF of (c₁) . ((c₂₅ * c₂₃),c₂₄) is Element of the carrier of (c₁)
K23((c₂₅ * c₂₃),c₂₄) is set
the multF of (c₁) . K23((c₂₅ * c₂₃),c₂₄) is set
c₂₆ is Element of the carrier of (c₁)
c₂₇ is Element of the carrier of (c₁)
c₂₆ * c₂₇ is Element of the carrier of (c₁)
the multF of (c₁) . (c₂₆,c₂₇) is Element of the carrier of (c₁)
K23(c₂₆,c₂₇) is set
the multF of (c₁) . K23(c₂₆,c₂₇) is set
c₂₈ is complex Element of COMPLEX
c₂₉ is complex Element of COMPLEX
c₂₈ * c₂₉ is complex Element of COMPLEX
(c₂₈ * c₂₉) * (c₂₆ * c₂₇) is Element of the carrier of (c₁)
K23((c₂₈ * c₂₉),(c₂₆ * c₂₇)) is set
the Mult of (c₁) . K23((c₂₈ * c₂₉),(c₂₆ * c₂₇)) is set
c₂₈ * c₂₆ is Element of the carrier of (c₁)
K23(c₂₈,c₂₆) is set
the Mult of (c₁) . K23(c₂₈,c₂₆) is set
c₂₉ * c₂₇ is Element of the carrier of (c₁)
K23(c₂₉,c₂₇) is set
the Mult of (c₁) . K23(c₂₉,c₂₇) is set
(c₂₈ * c₂₆) * (c₂₉ * c₂₇) is Element of the carrier of (c₁)
the multF of (c₁) . ((c₂₈ * c₂₆),(c₂₉ * c₂₇)) is Element of the carrier of (c₁)
K23((c₂₈ * c₂₆),(c₂₉ * c₂₇)) is set
the multF of (c₁) . K23((c₂₈ * c₂₆),(c₂₉ * c₂₇)) is set
c₃₀ is Element of the carrier of (c₁)
c₃₁ is Element of the carrier of (c₁)
c₃₀ + c₃₁ is Element of the carrier of (c₁)
the addF of (c₁) . (c₃₀,c₃₁) is Element of the carrier of (c₁)
K23(c₃₀,c₃₁) is set
the addF of (c₁) . K23(c₃₀,c₃₁) is set
c₃₂ is complex Element of COMPLEX
c₃₂ * (c₃₀ + c₃₁) is Element of the carrier of (c₁)
K23(c₃₂,(c₃₀ + c₃₁)) is set
the Mult of (c₁) . K23(c₃₂,(c₃₀ + c₃₁)) is set
c₃₂ * c₃₀ is Element of the carrier of (c₁)
K23(c₃₂,c₃₀) is set
the Mult of (c₁) . K23(c₃₂,c₃₀) is set
c₃₂ * c₃₁ is Element of the carrier of (c₁)
K23(c₃₂,c₃₁) is set
the Mult of (c₁) . K23(c₃₂,c₃₁) is set
(c₃₂ * c₃₀) + (c₃₂ * c₃₁) is Element of the carrier of (c₁)
the addF of (c₁) . ((c₃₂ * c₃₀),(c₃₂ * c₃₁)) is Element of the carrier of (c₁)
K23((c₃₂ * c₃₀),(c₃₂ * c₃₁)) is set
the addF of (c₁) . K23((c₃₂ * c₃₀),(c₃₂ * c₃₁)) is set
c₃₃ is Element of the carrier of (c₁)
c₃₄ is complex Element of COMPLEX
c₃₅ is complex Element of COMPLEX
c₃₄ + c₃₅ is complex Element of COMPLEX
(c₃₄ + c₃₅) * c₃₃ is Element of the carrier of (c₁)
K23((c₃₄ + c₃₅),c₃₃) is set
the Mult of (c₁) . K23((c₃₄ + c₃₅),c₃₃) is set
c₃₄ * c₃₃ is Element of the carrier of (c₁)
K23(c₃₄,c₃₃) is set
the Mult of (c₁) . K23(c₃₄,c₃₃) is set
c₃₅ * c₃₃ is Element of the carrier of (c₁)
K23(c₃₅,c₃₃) is set
the Mult of (c₁) . K23(c₃₅,c₃₃) is set
(c₃₄ * c₃₃) + (c₃₅ * c₃₃) is Element of the carrier of (c₁)
the addF of (c₁) . ((c₃₄ * c₃₃),(c₃₅ * c₃₃)) is Element of the carrier of (c₁)
K23((c₃₄ * c₃₃),(c₃₅ * c₃₃)) is set
the addF of (c₁) . K23((c₃₄ * c₃₃),(c₃₅ * c₃₃)) is set
c₃₆ is Element of the carrier of (c₁)
c₃₇ is complex Element of COMPLEX
c₃₈ is complex Element of COMPLEX
c₃₇ * c₃₈ is complex Element of COMPLEX
(c₃₇ * c₃₈) * c₃₆ is Element of the carrier of (c₁)
K23((c₃₇ * c₃₈),c₃₆) is set
the Mult of (c₁) . K23((c₃₇ * c₃₈),c₃₆) is set
c₃₈ * c₃₆ is Element of the carrier of (c₁)
K23(c₃₈,c₃₆) is set
the Mult of (c₁) . K23(c₃₈,c₃₆) is set
c₃₇ * (c₃₈ * c₃₆) is Element of the carrier of (c₁)
K23(c₃₇,(c₃₈ * c₃₆)) is set
the Mult of (c₁) . K23(c₃₇,(c₃₈ * c₃₆)) is set
c₃₉ is Element of the carrier of (c₁)
1r * c₃₉ is Element of the carrier of (c₁)
K23(1r,c₃₉) is set
the Mult of (c₁) . K23(1r,c₃₉) is set
c₄₁ is Element of the carrier of (c₁)
c₄₂ is Element of the carrier of (c₁)
c₄₁ + c₄₂ is Element of the carrier of (c₁)
the addF of (c₁) . (c₄₁,c₄₂) is Element of the carrier of (c₁)
K23(c₄₁,c₄₂) is set
the addF of (c₁) . K23(c₄₁,c₄₂) is set
c₄₀ is complex set
c₄₀ * (c₄₁ + c₄₂) is Element of the carrier of (c₁)
K23(c₄₀,(c₄₁ + c₄₂)) is set
the Mult of (c₁) . K23(c₄₀,(c₄₁ + c₄₂)) is set
c₄₀ * c₄₁ is Element of the carrier of (c₁)
K23(c₄₀,c₄₁) is set
the Mult of (c₁) . K23(c₄₀,c₄₁) is set
c₄₀ * c₄₂ is Element of the carrier of (c₁)
K23(c₄₀,c₄₂) is set
the Mult of (c₁) . K23(c₄₀,c₄₂) is set
(c₄₀ * c₄₁) + (c₄₀ * c₄₂) is Element of the carrier of (c₁)
the addF of (c₁) . ((c₄₀ * c₄₁),(c₄₀ * c₄₂)) is Element of the carrier of (c₁)
K23((c₄₀ * c₄₁),(c₄₀ * c₄₂)) is set
the addF of (c₁) . K23((c₄₀ * c₄₁),(c₄₀ * c₄₂)) is set
the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is non empty unital () ()
BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))
C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))
the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR is non empty set
ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) is set
Zero_ ((LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is V13() Function-like Element of LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )
Add_ ((LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is V13() V16([:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V17( LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Function-like V23([:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V27([:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):], LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Element of bool [:[:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]
[:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
[:[:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
bool [:[:(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
Mult_ ((LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is V13() V16([:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V17( LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Function-like V23([:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V27([:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):], LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Element of bool [:[:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]
[:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
[:[:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
bool [:[:COMPLEX,(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
CLSStruct(# (LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(Zero_ ((LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )))),(Add_ ((LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )))),(Mult_ ((LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) is set
( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is V13() V16([:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V17( BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Function-like V23([:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V27([:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):], BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]
[:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
[:[:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
bool [:[:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
Add_ ((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is V13() V16([:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V17( BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Function-like V23([:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V27([:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):], BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]
Mult_ ((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is V13() V16([:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V17( BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Function-like V23([:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]) V27([:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):], BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) Element of bool [:[:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):]
[:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
[:[:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
bool [:[:COMPLEX,(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):],(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )):] is set
( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is Element of BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )
id the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR is non empty V13() V16( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) V17( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) Function-like one-to-one V23( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) V27( the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) Element of bool [: the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR :]
[: the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR :] is set
bool [: the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the carrier of the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR :] is set
Zero_ ((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is Element of BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )
BoundedLinearOperatorsNorm ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ) is non empty V13() V16( BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) V17( REAL ) Function-like V23( BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )) V27( BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),REAL:]
[:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),REAL:] is set
((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ),(Add_ ((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )))),(Mult_ ((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )))),( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ),(Zero_ ((BoundedLinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR )))),(BoundedLinearOperatorsNorm ( the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR , the non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR ))) is () ()
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty unital () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like associative right-distributive right_unital vector-associative ()
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like associative right-distributive right_unital vector-associative ()
c₁ is non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR
(c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like unital associative right-distributive right_unital vector-associative () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty non trivial set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
C_NormSpace_of_BoundedLinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR
CNORMSTR(# (BoundedLinearOperators (c₁,c₁)),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁)) #) is non empty strict CNORMSTR
the carrier of (c₁) is non empty set
seq is right_complementable Element of the carrier of (c₁)
seq1 is right_complementable Element of the carrier of (c₁)
seq * seq1 is right_complementable Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (seq,seq1) is right_complementable Element of the carrier of (c₁)
K23(seq,seq1) is set
the multF of (c₁) . K23(seq,seq1) is set
||.(seq * seq1).|| is complex real ext-real Element of REAL
the normF of (c₁) is non empty V13() V16( the carrier of (c₁)) V17( REAL ) Function-like V23( the carrier of (c₁)) V27( the carrier of (c₁), REAL ) V35() V36() V37() Element of bool [: the carrier of (c₁),REAL:]
[: the carrier of (c₁),REAL:] is V35() V36() V37() set
bool [: the carrier of (c₁),REAL:] is set
the normF of (c₁) . (seq * seq1) is complex real ext-real Element of REAL
||.seq.|| is complex real ext-real Element of REAL
the normF of (c₁) . seq is complex real ext-real Element of REAL
||.seq1.|| is complex real ext-real Element of REAL
the normF of (c₁) . seq1 is complex real ext-real Element of REAL
||.seq.|| * ||.seq1.|| is complex real ext-real Element of REAL
g1 is Element of BoundedLinearOperators (c₁,c₁)
modetrans (g1,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(BoundedLinearOperatorsNorm (c₁,c₁)) . (modetrans (g1,c₁,c₁)) is complex real ext-real set
g is Element of BoundedLinearOperators (c₁,c₁)
modetrans (g,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(BoundedLinearOperatorsNorm (c₁,c₁)) . (modetrans (g,c₁,c₁)) is complex real ext-real set
((BoundedLinearOperatorsNorm (c₁,c₁)) . (modetrans (g1,c₁,c₁))) * ((BoundedLinearOperatorsNorm (c₁,c₁)) . (modetrans (g,c₁,c₁))) is complex real ext-real set
(BoundedLinearOperatorsNorm (c₁,c₁)) . g1 is complex real ext-real Element of REAL
((BoundedLinearOperatorsNorm (c₁,c₁)) . g1) * ((BoundedLinearOperatorsNorm (c₁,c₁)) . (modetrans (g,c₁,c₁))) is complex real ext-real Element of REAL
(c₁,g,g1) is Element of BoundedLinearOperators (c₁,c₁)
(c₁,(modetrans (g,c₁,c₁)),(modetrans (g1,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(BoundedLinearOperatorsNorm (c₁,c₁)) . (c₁,g,g1) is complex real ext-real Element of REAL
(BoundedLinearOperatorsNorm (c₁,c₁)) . (c₁,(modetrans (g,c₁,c₁)),(modetrans (g1,c₁,c₁))) is complex real ext-real set
1. (c₁) is right_complementable Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
the OneF of (c₁) is right_complementable Element of the carrier of (c₁)
||.(1. (c₁)).|| is complex real ext-real Element of REAL
the normF of (c₁) is non empty V13() V16( the carrier of (c₁)) V17( REAL ) Function-like V23( the carrier of (c₁)) V27( the carrier of (c₁), REAL ) V35() V36() V37() Element of bool [: the carrier of (c₁),REAL:]
[: the carrier of (c₁),REAL:] is V35() V36() V37() set
bool [: the carrier of (c₁),REAL:] is set
the normF of (c₁) . (1. (c₁)) is complex real ext-real Element of REAL
seq is complex set
seq1 is right_complementable Element of the carrier of (c₁)
g1 is right_complementable Element of the carrier of (c₁)
seq1 * g1 is right_complementable Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . (seq1,g1) is right_complementable Element of the carrier of (c₁)
K23(seq1,g1) is set
the multF of (c₁) . K23(seq1,g1) is set
seq * (seq1 * g1) is right_complementable Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23(seq,(seq1 * g1)) is set
the Mult of (c₁) . K23(seq,(seq1 * g1)) is set
seq * g1 is right_complementable Element of the carrier of (c₁)
K23(seq,g1) is set
the Mult of (c₁) . K23(seq,g1) is set
seq1 * (seq * g1) is right_complementable Element of the carrier of (c₁)
the multF of (c₁) . (seq1,(seq * g1)) is right_complementable Element of the carrier of (c₁)
K23(seq1,(seq * g1)) is set
the multF of (c₁) . K23(seq1,(seq * g1)) is set
1r * seq is complex set
(1r * seq) * (seq1 * g1) is right_complementable Element of the carrier of (c₁)
K23((1r * seq),(seq1 * g1)) is set
the Mult of (c₁) . K23((1r * seq),(seq1 * g1)) is set
1r * seq1 is right_complementable Element of the carrier of (c₁)
K23(1r,seq1) is set
the Mult of (c₁) . K23(1r,seq1) is set
(1r * seq1) * (seq * g1) is right_complementable Element of the carrier of (c₁)
the multF of (c₁) . ((1r * seq1),(seq * g1)) is right_complementable Element of the carrier of (c₁)
K23((1r * seq1),(seq * g1)) is set
the multF of (c₁) . K23((1r * seq1),(seq * g1)) is set
seq is right_complementable Element of the carrier of (c₁)
(1. (c₁)) * seq is right_complementable Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the multF of (c₁) . ((1. (c₁)),seq) is right_complementable Element of the carrier of (c₁)
K23((1. (c₁)),seq) is set
the multF of (c₁) . K23((1. (c₁)),seq) is set
seq1 is Element of BoundedLinearOperators (c₁,c₁)
(c₁,seq1,(c₁)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (seq1,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (seq1,c₁,c₁)),(modetrans ((c₁),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
seq1 is right_complementable Element of the carrier of (c₁)
g1 is right_complementable Element of the carrier of (c₁)
seq1 + g1 is right_complementable Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . (seq1,g1) is right_complementable Element of the carrier of (c₁)
K23(seq1,g1) is set
the addF of (c₁) . K23(seq1,g1) is set
seq is right_complementable Element of the carrier of (c₁)
(seq1 + g1) * seq is right_complementable Element of the carrier of (c₁)
the multF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
the multF of (c₁) . ((seq1 + g1),seq) is right_complementable Element of the carrier of (c₁)
K23((seq1 + g1),seq) is set
the multF of (c₁) . K23((seq1 + g1),seq) is set
seq1 * seq is right_complementable Element of the carrier of (c₁)
the multF of (c₁) . (seq1,seq) is right_complementable Element of the carrier of (c₁)
K23(seq1,seq) is set
the multF of (c₁) . K23(seq1,seq) is set
g1 * seq is right_complementable Element of the carrier of (c₁)
the multF of (c₁) . (g1,seq) is right_complementable Element of the carrier of (c₁)
K23(g1,seq) is set
the multF of (c₁) . K23(g1,seq) is set
(seq1 * seq) + (g1 * seq) is right_complementable Element of the carrier of (c₁)
the addF of (c₁) . ((seq1 * seq),(g1 * seq)) is right_complementable Element of the carrier of (c₁)
K23((seq1 * seq),(g1 * seq)) is set
the addF of (c₁) . K23((seq1 * seq),(g1 * seq)) is set
seq1 + g1 is right_complementable Element of the carrier of (c₁)
(seq1 + g1) * seq is right_complementable Element of the carrier of (c₁)
the multF of (c₁) . ((seq1 + g1),seq) is right_complementable Element of the carrier of (c₁)
K23((seq1 + g1),seq) is set
the multF of (c₁) . K23((seq1 + g1),seq) is set
g is Element of BoundedLinearOperators (c₁,c₁)
r is Element of BoundedLinearOperators (c₁,c₁)
m is Element of BoundedLinearOperators (c₁,c₁)
(c₁,r,m) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . (r,m) is Element of BoundedLinearOperators (c₁,c₁)
K23(r,m) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23(r,m) is set
(c₁,g,(c₁,r,m)) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (g,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
modetrans ((c₁,r,m),c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans ((c₁,r,m),c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,g,r) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (r,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans (r,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,g,m) is Element of BoundedLinearOperators (c₁,c₁)
modetrans (m,c₁,c₁) is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(modetrans (g,c₁,c₁)),(modetrans (m,c₁,c₁))) is non empty V13() V16( the carrier of c₁) V16( the carrier of c₁) V17( the carrier of c₁) V17( the carrier of c₁) Function-like V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) V171(c₁,c₁) V172(c₁,c₁) Lipschitzian Element of bool [: the carrier of c₁, the carrier of c₁:]
(c₁,(c₁,g,r),(c₁,g,m)) is Element of BoundedLinearOperators (c₁,c₁)
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,g,r),(c₁,g,m)) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,g,r),(c₁,g,m)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,g,r),(c₁,g,m)) is set
(c₁) . (m,g) is Element of BoundedLinearOperators (c₁,c₁)
K23(m,g) is set
(c₁) . K23(m,g) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((c₁,g,r),((c₁) . (m,g))) is Element of BoundedLinearOperators (c₁,c₁)
K23((c₁,g,r),((c₁) . (m,g))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((c₁,g,r),((c₁) . (m,g))) is set
(seq1 * seq) + (g1 * seq) is right_complementable Element of the carrier of (c₁)
[:NAT, the carrier of (c₁):] is set
bool [:NAT, the carrier of (c₁):] is set
seq is non empty V13() V16( NAT ) V17( the carrier of (c₁)) Function-like V23( NAT ) V27( NAT , the carrier of (c₁)) Element of bool [:NAT, the carrier of (c₁):]
the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty set
[:NAT, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:NAT, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
g1 is complex real ext-real Element of REAL
g is epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real V57() V58() V59() V60() V61() V62() Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real V57() V58() V59() V60() V61() V62() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real V57() V58() V59() V60() V61() V62() Element of NAT
seq1 is non empty V13() V16( NAT ) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23( NAT ) V27( NAT , the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:NAT, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
seq1 . r is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
seq1 . m is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
(seq1 . r) - (seq1 . m) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
- (seq1 . m) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
(seq1 . r) + (- (seq1 . m)) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . ((seq1 . r),(- (seq1 . m))) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23((seq1 . r),(- (seq1 . m))) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23((seq1 . r),(- (seq1 . m))) is set
||.((seq1 . r) - (seq1 . m)).|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is non empty V13() V16( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V17( REAL ) Function-like V23( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) V27( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)), REAL ) V35() V36() V37() Element of bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:]
[: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [: the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)),REAL:] is set
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . ((seq1 . r) - (seq1 . m)) is complex real ext-real Element of REAL
(- 1r) * (seq1 . m) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) is V13() V16([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V17( the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Function-like V23([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))) Element of bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX, the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):], the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)):] is set
K23((- 1r),(seq1 . m)) is set
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23((- 1r),(seq1 . m)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((seq1 . r),((- 1r) * (seq1 . m))) is set
K23((seq1 . r),((- 1r) * (seq1 . m))) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((seq1 . r),((- 1r) * (seq1 . m))) is set
(BoundedLinearOperatorsNorm (c₁,c₁)) . ((Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((seq1 . r),((- 1r) * (seq1 . m)))) is complex real ext-real set
seq . r is right_complementable Element of the carrier of (c₁)
seq . m is right_complementable Element of the carrier of (c₁)
(- 1r) * (seq . m) is right_complementable Element of the carrier of (c₁)
the Mult of (c₁) is V13() V16([:COMPLEX, the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([:COMPLEX, the carrier of (c₁):]) V27([:COMPLEX, the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):]
[:COMPLEX, the carrier of (c₁):] is set
[:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[:COMPLEX, the carrier of (c₁):], the carrier of (c₁):] is set
K23((- 1r),(seq . m)) is set
the Mult of (c₁) . K23((- 1r),(seq . m)) is set
(seq . r) + ((- 1r) * (seq . m)) is right_complementable Element of the carrier of (c₁)
the addF of (c₁) is V13() V16([: the carrier of (c₁), the carrier of (c₁):]) V17( the carrier of (c₁)) Function-like V23([: the carrier of (c₁), the carrier of (c₁):]) V27([: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁)) Element of bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):]
[: the carrier of (c₁), the carrier of (c₁):] is set
[:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
bool [:[: the carrier of (c₁), the carrier of (c₁):], the carrier of (c₁):] is set
the addF of (c₁) . ((seq . r),((- 1r) * (seq . m))) is right_complementable Element of the carrier of (c₁)
K23((seq . r),((- 1r) * (seq . m))) is set
the addF of (c₁) . K23((seq . r),((- 1r) * (seq . m))) is set
(BoundedLinearOperatorsNorm (c₁,c₁)) . ((seq . r) + ((- 1r) * (seq . m))) is complex real ext-real set
(seq . r) - (seq . m) is right_complementable Element of the carrier of (c₁)
- (seq . m) is right_complementable Element of the carrier of (c₁)
(seq . r) + (- (seq . m)) is right_complementable Element of the carrier of (c₁)
the addF of (c₁) . ((seq . r),(- (seq . m))) is right_complementable Element of the carrier of (c₁)
K23((seq . r),(- (seq . m))) is set
the addF of (c₁) . K23((seq . r),(- (seq . m))) is set
||.((seq . r) - (seq . m)).|| is complex real ext-real Element of REAL
the normF of (c₁) . ((seq . r) - (seq . m)) is complex real ext-real Element of REAL
g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
r is complex real ext-real Element of REAL
m is epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real V57() V58() V59() V60() V61() V62() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real V30() V31() ext-real V57() V58() V59() V60() V61() V62() Element of NAT
seq1 . n is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
(seq1 . n) - g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
- g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
(seq1 . n) + (- g1) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . ((seq1 . n),(- g1)) is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23((seq1 . n),(- g1)) is set
the addF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23((seq1 . n),(- g1)) is set
||.((seq1 . n) - g1).|| is complex real ext-real Element of REAL
the normF of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . ((seq1 . n) - g1) is complex real ext-real Element of REAL
(- 1r) * g1 is V13() Function-like right_complementable Element of the carrier of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁))
K23((- 1r),g1) is set
the Mult of (C_NormSpace_of_BoundedLinearOperators (c₁,c₁)) . K23((- 1r),g1) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((seq1 . n),((- 1r) * g1)) is set
K23((seq1 . n),((- 1r) * g1)) is set
(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . K23((seq1 . n),((- 1r) * g1)) is set
(BoundedLinearOperatorsNorm (c₁,c₁)) . ((Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) . ((seq1 . n),((- 1r) * g1))) is complex real ext-real set
seq . n is right_complementable Element of the carrier of (c₁)
g is right_complementable Element of the carrier of (c₁)
(- 1r) * g is right_complementable Element of the carrier of (c₁)
K23((- 1r),g) is set
the Mult of (c₁) . K23((- 1r),g) is set
(seq . n) + ((- 1r) * g) is right_complementable Element of the carrier of (c₁)
the addF of (c₁) . ((seq . n),((- 1r) * g)) is right_complementable Element of the carrier of (c₁)
K23((seq . n),((- 1r) * g)) is set
the addF of (c₁) . K23((seq . n),((- 1r) * g)) is set
(BoundedLinearOperatorsNorm (c₁,c₁)) . ((seq . n) + ((- 1r) * g)) is complex real ext-real set
(seq . n) - g is right_complementable Element of the carrier of (c₁)
- g is right_complementable Element of the carrier of (c₁)
(seq . n) + (- g) is right_complementable Element of the carrier of (c₁)
the addF of (c₁) . ((seq . n),(- g)) is right_complementable Element of the carrier of (c₁)
K23((seq . n),(- g)) is set
the addF of (c₁) . K23((seq . n),(- g)) is set
||.((seq . n) - g).|| is complex real ext-real Element of REAL
the normF of (c₁) . ((seq . n) - g) is complex real ext-real Element of REAL
the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR is non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR
( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like unital associative right-distributive left-distributive right_unital left_unital complete vector-associative () () () () () ()
BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))
C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))
the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR is non empty non trivial set
ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) is set
Zero_ ((LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is V13() Function-like Element of LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )
Add_ ((LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is V13() V16([:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V17( LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Function-like V23([:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V27([:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):], LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Element of bool [:[:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]
[:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
[:[:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
bool [:[:(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
Mult_ ((LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is V13() V16([:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V17( LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Function-like V23([:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V27([:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):], LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Element of bool [:[:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]
[:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
[:[:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
bool [:[:COMPLEX,(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
CLSStruct(# (LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(Zero_ ((LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )))),(Add_ ((LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )))),(Mult_ ((LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(ComplexVectSpace ( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) is set
( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is V13() V16([:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V17( BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Function-like V23([:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V27([:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):], BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]
[:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
[:[:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
bool [:[:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
Add_ ((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is V13() V16([:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V17( BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Function-like V23([:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V27([:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):], BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]
Mult_ ((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is V13() V16([:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V17( BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Function-like V23([:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]) V27([:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):], BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) Element of bool [:[:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):]
[:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
[:[:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
bool [:[:COMPLEX,(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):],(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )):] is set
( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is Element of BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )
id the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR is non empty V13() V16( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) V17( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) Function-like one-to-one V23( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) V27( the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) Element of bool [: the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR :]
[: the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR :] is set
bool [: the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the carrier of the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR :] is set
Zero_ ((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is Element of BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )
BoundedLinearOperatorsNorm ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ) is non empty V13() V16( BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) V17( REAL ) Function-like V23( BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )) V27( BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),REAL:]
[:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),REAL:] is set
((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ),(Add_ ((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )))),(Mult_ ((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )))),( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ),(Zero_ ((BoundedLinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )),(C_VectorSpace_of_LinearOperators ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR )))),(BoundedLinearOperatorsNorm ( the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR , the non empty non trivial right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like complete CNORMSTR ))) is () ()
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty right_complementable strict Abelian add-associative right_zeroed unital associative well-unital distributive doubleLoopStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
doubleLoopStr(# (BoundedLinearOperators (c₁,c₁)),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is non empty strict doubleLoopStr
1. (c₁) is right_complementable Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
the OneF of (c₁) is right_complementable Element of the carrier of (c₁)
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative unital associative right-distributive right_unital strict vector-associative ComplexAlgebraStr
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
ComplexAlgebraStr(# (BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))) #) is strict ComplexAlgebraStr
1. (c₁) is right_complementable Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
the OneF of (c₁) is right_complementable Element of the carrier of (c₁)
c₁ is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like CNORMSTR
(c₁) is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive vector-distributive scalar-distributive scalar-associative scalar-unital ComplexNormSpace-like unital associative right-distributive right_unital vector-associative () ()
BoundedLinearOperators (c₁,c₁) is non empty Element of bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁))
C_VectorSpace_of_LinearOperators (c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
LinearOperators (c₁,c₁) is non empty functional Element of bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁))
the carrier of c₁ is non empty set
ComplexVectSpace ( the carrier of c₁,c₁) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is non empty set
bool the carrier of (ComplexVectSpace ( the carrier of c₁,c₁)) is set
Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() Function-like Element of LinearOperators (c₁,c₁)
Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):]) V27([:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):] is set
[:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:(LinearOperators (c₁,c₁)),(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁))) is V13() V16([:COMPLEX,(LinearOperators (c₁,c₁)):]) V17( LinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(LinearOperators (c₁,c₁)):]) V27([:COMPLEX,(LinearOperators (c₁,c₁)):], LinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):]
[:COMPLEX,(LinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(LinearOperators (c₁,c₁)):],(LinearOperators (c₁,c₁)):] is set
CLSStruct(# (LinearOperators (c₁,c₁)),(Zero_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Add_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))),(Mult_ ((LinearOperators (c₁,c₁)),(ComplexVectSpace ( the carrier of c₁,c₁)))) #) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is non empty set
bool the carrier of (C_VectorSpace_of_LinearOperators (c₁,c₁)) is set
(c₁) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):] is set
[:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):]) V27([:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:(BoundedLinearOperators (c₁,c₁)),(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is V13() V16([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V17( BoundedLinearOperators (c₁,c₁)) Function-like V23([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):]) V27([:COMPLEX,(BoundedLinearOperators (c₁,c₁)):], BoundedLinearOperators (c₁,c₁)) Element of bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):]
[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):] is set
[:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
bool [:[:COMPLEX,(BoundedLinearOperators (c₁,c₁)):],(BoundedLinearOperators (c₁,c₁)):] is set
(c₁) is Element of BoundedLinearOperators (c₁,c₁)
id the carrier of c₁ is non empty V13() V16( the carrier of c₁) V17( the carrier of c₁) Function-like one-to-one V23( the carrier of c₁) V27( the carrier of c₁, the carrier of c₁) Element of bool [: the carrier of c₁, the carrier of c₁:]
[: the carrier of c₁, the carrier of c₁:] is set
bool [: the carrier of c₁, the carrier of c₁:] is set
Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁))) is Element of BoundedLinearOperators (c₁,c₁)
BoundedLinearOperatorsNorm (c₁,c₁) is non empty V13() V16( BoundedLinearOperators (c₁,c₁)) V17( REAL ) Function-like V23( BoundedLinearOperators (c₁,c₁)) V27( BoundedLinearOperators (c₁,c₁), REAL ) V35() V36() V37() Element of bool [:(BoundedLinearOperators (c₁,c₁)),REAL:]
[:(BoundedLinearOperators (c₁,c₁)),REAL:] is V35() V36() V37() set
bool [:(BoundedLinearOperators (c₁,c₁)),REAL:] is set
((BoundedLinearOperators (c₁,c₁)),(c₁),(Add_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(Mult_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(c₁),(Zero_ ((BoundedLinearOperators (c₁,c₁)),(C_VectorSpace_of_LinearOperators (c₁,c₁)))),(BoundedLinearOperatorsNorm (c₁,c₁))) is () ()
1. (c₁) is right_complementable Element of the carrier of (c₁)
the carrier of (c₁) is non empty set
the OneF of (c₁) is right_complementable Element of the carrier of (c₁)