:: LOPBAN_2 semantic presentation

REAL is non empty V46() V51() V52() V53() V57() set
NAT is V51() V52() V53() V54() V55() V56() V57() Element of bool REAL
bool REAL is set
COMPLEX is non empty V46() V51() V57() set
RAT is non empty V46() V51() V52() V53() V54() V57() set
INT is non empty V46() V51() V52() V53() V54() V55() V57() set
[:COMPLEX,COMPLEX:] is V15() V36() set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is V15() V36() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is V15() V36() V37() V38() set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is V15() V36() V37() V38() set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is V15() V19( RAT ) V36() V37() V38() set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is V15() V19( RAT ) V36() V37() V38() set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is V15() V19( RAT ) V19( INT ) V36() V37() V38() set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is V15() V19( RAT ) V19( INT ) V36() V37() V38() set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is V15() V19( RAT ) V19( INT ) V36() V37() V38() V39() set
[:[:NAT,NAT:],NAT:] is V15() V19( RAT ) V19( INT ) V36() V37() V38() V39() set
bool [:[:NAT,NAT:],NAT:] is set
[:NAT,REAL:] is V15() V36() V37() V38() set
bool [:NAT,REAL:] is set
omega is V51() V52() V53() V54() V55() V56() V57() set
bool omega is set
bool NAT is set
the_set_of_RealSequences is non empty set
[:the_set_of_RealSequences,the_set_of_RealSequences:] is V15() set
[:[:the_set_of_RealSequences,the_set_of_RealSequences:],the_set_of_RealSequences:] is V15() set
bool [:[:the_set_of_RealSequences,the_set_of_RealSequences:],the_set_of_RealSequences:] is set
[:REAL,the_set_of_RealSequences:] is V15() set
[:[:REAL,the_set_of_RealSequences:],the_set_of_RealSequences:] is V15() set
bool [:[:REAL,the_set_of_RealSequences:],the_set_of_RealSequences:] is set
Linear_Space_of_RealSequences is RLSStruct
the carrier of Linear_Space_of_RealSequences is set
bool the carrier of Linear_Space_of_RealSequences is set
the_set_of_l2RealSequences is Element of bool the carrier of Linear_Space_of_RealSequences
[:the_set_of_l2RealSequences,the_set_of_l2RealSequences:] is V15() set
[:[:the_set_of_l2RealSequences,the_set_of_l2RealSequences:],REAL:] is V15() V36() V37() V38() set
bool [:[:the_set_of_l2RealSequences,the_set_of_l2RealSequences:],REAL:] is set
the_set_of_l1RealSequences is non empty Element of bool the carrier of Linear_Space_of_RealSequences
[:the_set_of_l1RealSequences,REAL:] is V15() V36() V37() V38() set
bool [:the_set_of_l1RealSequences,REAL:] is set
[:COMPLEX,REAL:] is V15() V36() V37() V38() set
bool [:COMPLEX,REAL:] is set
{} is empty V15() non-empty empty-yielding V19( RAT ) Function-like one-to-one constant functional V36() V37() V38() V39() V51() V52() V53() V54() V55() V56() V57() set
1 is non empty natural V11() real V13() V32() ext-real positive non negative V51() V52() V53() V54() V55() V56() Element of NAT
0 is empty natural V11() real V13() V15() non-empty empty-yielding V19( RAT ) Function-like one-to-one constant functional V32() ext-real non positive non negative V36() V37() V38() V39() V51() V52() V53() V54() V55() V56() V57() Element of NAT
- 1 is V11() real ext-real non positive Element of REAL
Zeroseq is Element of the_set_of_RealSequences
l1_Space is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of l1_Space is non empty set
0. l1_Space is V80( l1_Space ) left_complementable right_complementable complementable Element of the carrier of l1_Space
the ZeroF of l1_Space is left_complementable right_complementable complementable Element of the carrier of l1_Space
[:NAT, the carrier of l1_Space:] is V15() set
bool [:NAT, the carrier of l1_Space:] is set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of X is non empty set
c₂ is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of c₂ is non empty set
[: the carrier of X, the carrier of c₂:] is V15() set
bool [: the carrier of X, the carrier of c₂:] is set
UNIT is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of UNIT is non empty set
[: the carrier of c₂, the carrier of UNIT:] is V15() set
bool [: the carrier of c₂, the carrier of UNIT:] is set
[: the carrier of X, the carrier of UNIT:] is V15() set
bool [: the carrier of X, the carrier of UNIT:] is set
MULT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of c₂) V165(X,c₂) V166(X,c₂) Element of bool [: the carrier of X, the carrier of c₂:]
ADD is non empty V15() Function-like V25( the carrier of c₂) V29( the carrier of c₂, the carrier of UNIT) V165(c₂,UNIT) V166(c₂,UNIT) Element of bool [: the carrier of c₂, the carrier of UNIT:]
ADD * MULT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of UNIT) Element of bool [: the carrier of X, the carrier of UNIT:]
BS is left_complementable right_complementable complementable Element of the carrier of X
BLOP is V11() real ext-real Element of REAL
BLOP * BS is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X is V15() Function-like V25([:REAL, the carrier of X:]) V29([:REAL, the carrier of X:], the carrier of X) Element of bool [:[:REAL, the carrier of X:], the carrier of X:]
[:REAL, the carrier of X:] is V15() set
[:[:REAL, the carrier of X:], the carrier of X:] is V15() set
bool [:[:REAL, the carrier of X:], the carrier of X:] is set
the Mult of X . (BLOP,BS) is set
(ADD * MULT) . (BLOP * BS) is left_complementable right_complementable complementable Element of the carrier of UNIT
MULT . (BLOP * BS) is left_complementable right_complementable complementable Element of the carrier of c₂
ADD . (MULT . (BLOP * BS)) is left_complementable right_complementable complementable Element of the carrier of UNIT
MULT . BS is left_complementable right_complementable complementable Element of the carrier of c₂
BLOP * (MULT . BS) is left_complementable right_complementable complementable Element of the carrier of c₂
the Mult of c₂ is V15() Function-like V25([:REAL, the carrier of c₂:]) V29([:REAL, the carrier of c₂:], the carrier of c₂) Element of bool [:[:REAL, the carrier of c₂:], the carrier of c₂:]
[:REAL, the carrier of c₂:] is V15() set
[:[:REAL, the carrier of c₂:], the carrier of c₂:] is V15() set
bool [:[:REAL, the carrier of c₂:], the carrier of c₂:] is set
the Mult of c₂ . (BLOP,(MULT . BS)) is set
ADD . (BLOP * (MULT . BS)) is left_complementable right_complementable complementable Element of the carrier of UNIT
ADD . (MULT . BS) is left_complementable right_complementable complementable Element of the carrier of UNIT
BLOP * (ADD . (MULT . BS)) is left_complementable right_complementable complementable Element of the carrier of UNIT
the Mult of UNIT is V15() Function-like V25([:REAL, the carrier of UNIT:]) V29([:REAL, the carrier of UNIT:], the carrier of UNIT) Element of bool [:[:REAL, the carrier of UNIT:], the carrier of UNIT:]
[:REAL, the carrier of UNIT:] is V15() set
[:[:REAL, the carrier of UNIT:], the carrier of UNIT:] is V15() set
bool [:[:REAL, the carrier of UNIT:], the carrier of UNIT:] is set
the Mult of UNIT . (BLOP,(ADD . (MULT . BS))) is set
(ADD * MULT) . BS is left_complementable right_complementable complementable Element of the carrier of UNIT
BLOP * ((ADD * MULT) . BS) is left_complementable right_complementable complementable Element of the carrier of UNIT
the Mult of UNIT . (BLOP,((ADD * MULT) . BS)) is set
BS is left_complementable right_complementable complementable Element of the carrier of X
BLOP is left_complementable right_complementable complementable Element of the carrier of X
BS + BLOP is left_complementable right_complementable complementable Element of the carrier of X
the addF of X is V15() Function-like V25([: the carrier of X, the carrier of X:]) V29([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is V15() set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the addF of X . (BS,BLOP) is left_complementable right_complementable complementable Element of the carrier of X
(ADD * MULT) . (BS + BLOP) is left_complementable right_complementable complementable Element of the carrier of UNIT
MULT . (BS + BLOP) is left_complementable right_complementable complementable Element of the carrier of c₂
ADD . (MULT . (BS + BLOP)) is left_complementable right_complementable complementable Element of the carrier of UNIT
MULT . BS is left_complementable right_complementable complementable Element of the carrier of c₂
MULT . BLOP is left_complementable right_complementable complementable Element of the carrier of c₂
(MULT . BS) + (MULT . BLOP) is left_complementable right_complementable complementable Element of the carrier of c₂
the addF of c₂ is V15() Function-like V25([: the carrier of c₂, the carrier of c₂:]) V29([: the carrier of c₂, the carrier of c₂:], the carrier of c₂) Element of bool [:[: the carrier of c₂, the carrier of c₂:], the carrier of c₂:]
[: the carrier of c₂, the carrier of c₂:] is V15() set
[:[: the carrier of c₂, the carrier of c₂:], the carrier of c₂:] is V15() set
bool [:[: the carrier of c₂, the carrier of c₂:], the carrier of c₂:] is set
the addF of c₂ . ((MULT . BS),(MULT . BLOP)) is left_complementable right_complementable complementable Element of the carrier of c₂
ADD . ((MULT . BS) + (MULT . BLOP)) is left_complementable right_complementable complementable Element of the carrier of UNIT
ADD . (MULT . BS) is left_complementable right_complementable complementable Element of the carrier of UNIT
ADD . (MULT . BLOP) is left_complementable right_complementable complementable Element of the carrier of UNIT
(ADD . (MULT . BS)) + (ADD . (MULT . BLOP)) is left_complementable right_complementable complementable Element of the carrier of UNIT
the addF of UNIT is V15() Function-like V25([: the carrier of UNIT, the carrier of UNIT:]) V29([: 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 V15() set
[:[: the carrier of UNIT, the carrier of UNIT:], the carrier of UNIT:] is V15() 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 left_complementable right_complementable complementable Element of the carrier of UNIT
(ADD * MULT) . BS is left_complementable right_complementable complementable Element of the carrier of UNIT
((ADD * MULT) . BS) + (ADD . (MULT . BLOP)) is left_complementable right_complementable complementable Element of the carrier of UNIT
the addF of UNIT . (((ADD * MULT) . BS),(ADD . (MULT . BLOP))) is left_complementable right_complementable complementable Element of the carrier of UNIT
(ADD * MULT) . BLOP is left_complementable right_complementable complementable Element of the carrier of UNIT
((ADD * MULT) . BS) + ((ADD * MULT) . BLOP) is left_complementable right_complementable complementable Element of the carrier of UNIT
the addF of UNIT . (((ADD * MULT) . BS),((ADD * MULT) . BLOP)) is left_complementable right_complementable complementable Element of the carrier of UNIT
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
c₂ is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of c₂ is non empty set
[: the carrier of X, the carrier of c₂:] is V15() set
bool [: the carrier of X, the carrier of c₂:] is set
UNIT is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of UNIT is non empty set
[: the carrier of c₂, the carrier of UNIT:] is V15() set
bool [: the carrier of c₂, the carrier of UNIT:] is set
[: the carrier of X, the carrier of UNIT:] is V15() set
bool [: the carrier of X, the carrier of UNIT:] is set
BoundedLinearOperatorsNorm (c₂,UNIT) is non empty V15() Function-like V25( BoundedLinearOperators (c₂,UNIT)) V29( BoundedLinearOperators (c₂,UNIT), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (c₂,UNIT)),REAL:]
BoundedLinearOperators (c₂,UNIT) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (c₂,UNIT))
R_VectorSpace_of_LinearOperators (c₂,UNIT) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (c₂,UNIT) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of c₂,UNIT))
RealVectSpace ( the carrier of c₂,UNIT) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of c₂, the carrier of UNIT) is non empty functional M4( the carrier of c₂, the carrier of UNIT)
FuncZero ( the carrier of c₂,UNIT) is V15() Function-like V25( the carrier of c₂) V29( the carrier of c₂, the carrier of UNIT) Element of K138( the carrier of c₂, the carrier of UNIT)
0. UNIT is V80(UNIT) left_complementable right_complementable complementable Element of the carrier of UNIT
the ZeroF of UNIT is left_complementable right_complementable complementable Element of the carrier of UNIT
K308( the carrier of UNIT, the carrier of c₂,(0. UNIT)) is non empty V15() Function-like V25( the carrier of c₂) V29( the carrier of c₂, the carrier of UNIT) Element of bool [: the carrier of c₂, the carrier of UNIT:]
FuncAdd ( the carrier of c₂,UNIT) is V15() Function-like V25([:K138( the carrier of c₂, the carrier of UNIT),K138( the carrier of c₂, the carrier of UNIT):]) V29([:K138( the carrier of c₂, the carrier of UNIT),K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT)) Element of bool [:[:K138( the carrier of c₂, the carrier of UNIT),K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT):]
[:K138( the carrier of c₂, the carrier of UNIT),K138( the carrier of c₂, the carrier of UNIT):] is V15() set
[:[:K138( the carrier of c₂, the carrier of UNIT),K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT):] is V15() set
bool [:[:K138( the carrier of c₂, the carrier of UNIT),K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT):] is set
FuncExtMult ( the carrier of c₂,UNIT) is V15() Function-like V25([:REAL,K138( the carrier of c₂, the carrier of UNIT):]) V29([:REAL,K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT)) Element of bool [:[:REAL,K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT):]
[:REAL,K138( the carrier of c₂, the carrier of UNIT):] is V15() set
[:[:REAL,K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT):] is V15() set
bool [:[:REAL,K138( the carrier of c₂, the carrier of UNIT):],K138( the carrier of c₂, the carrier of UNIT):] is set
RLSStruct(# K138( the carrier of c₂, the carrier of UNIT),(FuncZero ( the carrier of c₂,UNIT)),(FuncAdd ( the carrier of c₂,UNIT)),(FuncExtMult ( the carrier of c₂,UNIT)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of c₂,UNIT)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of c₂,UNIT)) is set
Zero_ ((LinearOperators (c₂,UNIT)),(RealVectSpace ( the carrier of c₂,UNIT))) is V15() Function-like Element of LinearOperators (c₂,UNIT)
Add_ ((LinearOperators (c₂,UNIT)),(RealVectSpace ( the carrier of c₂,UNIT))) is V15() Function-like V25([:(LinearOperators (c₂,UNIT)),(LinearOperators (c₂,UNIT)):]) V29([:(LinearOperators (c₂,UNIT)),(LinearOperators (c₂,UNIT)):], LinearOperators (c₂,UNIT)) Element of bool [:[:(LinearOperators (c₂,UNIT)),(LinearOperators (c₂,UNIT)):],(LinearOperators (c₂,UNIT)):]
[:(LinearOperators (c₂,UNIT)),(LinearOperators (c₂,UNIT)):] is V15() set
[:[:(LinearOperators (c₂,UNIT)),(LinearOperators (c₂,UNIT)):],(LinearOperators (c₂,UNIT)):] is V15() set
bool [:[:(LinearOperators (c₂,UNIT)),(LinearOperators (c₂,UNIT)):],(LinearOperators (c₂,UNIT)):] is set
Mult_ ((LinearOperators (c₂,UNIT)),(RealVectSpace ( the carrier of c₂,UNIT))) is V15() Function-like V25([:REAL,(LinearOperators (c₂,UNIT)):]) V29([:REAL,(LinearOperators (c₂,UNIT)):], LinearOperators (c₂,UNIT)) Element of bool [:[:REAL,(LinearOperators (c₂,UNIT)):],(LinearOperators (c₂,UNIT)):]
[:REAL,(LinearOperators (c₂,UNIT)):] is V15() set
[:[:REAL,(LinearOperators (c₂,UNIT)):],(LinearOperators (c₂,UNIT)):] is V15() set
bool [:[:REAL,(LinearOperators (c₂,UNIT)):],(LinearOperators (c₂,UNIT)):] is set
RLSStruct(# (LinearOperators (c₂,UNIT)),(Zero_ ((LinearOperators (c₂,UNIT)),(RealVectSpace ( the carrier of c₂,UNIT)))),(Add_ ((LinearOperators (c₂,UNIT)),(RealVectSpace ( the carrier of c₂,UNIT)))),(Mult_ ((LinearOperators (c₂,UNIT)),(RealVectSpace ( the carrier of c₂,UNIT)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (c₂,UNIT)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (c₂,UNIT)) is set
[:(BoundedLinearOperators (c₂,UNIT)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (c₂,UNIT)),REAL:] is set
BoundedLinearOperatorsNorm (X,c₂) is non empty V15() Function-like V25( BoundedLinearOperators (X,c₂)) V29( BoundedLinearOperators (X,c₂), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,c₂)),REAL:]
BoundedLinearOperators (X,c₂) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,c₂))
R_VectorSpace_of_LinearOperators (X,c₂) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,c₂) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,c₂))
RealVectSpace ( the carrier of X,c₂) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of c₂) is non empty functional M4( the carrier of X, the carrier of c₂)
FuncZero ( the carrier of X,c₂) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of c₂) Element of K138( the carrier of X, the carrier of c₂)
0. c₂ is V80(c₂) left_complementable right_complementable complementable Element of the carrier of c₂
the ZeroF of c₂ is left_complementable right_complementable complementable Element of the carrier of c₂
K308( the carrier of c₂, the carrier of X,(0. c₂)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of c₂) Element of bool [: the carrier of X, the carrier of c₂:]
FuncAdd ( the carrier of X,c₂) is V15() Function-like V25([:K138( the carrier of X, the carrier of c₂),K138( the carrier of X, the carrier of c₂):]) V29([:K138( the carrier of X, the carrier of c₂),K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂)) Element of bool [:[:K138( the carrier of X, the carrier of c₂),K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂):]
[:K138( the carrier of X, the carrier of c₂),K138( the carrier of X, the carrier of c₂):] is V15() set
[:[:K138( the carrier of X, the carrier of c₂),K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂):] is V15() set
bool [:[:K138( the carrier of X, the carrier of c₂),K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂):] is set
FuncExtMult ( the carrier of X,c₂) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of c₂):]) V29([:REAL,K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂):]
[:REAL,K138( the carrier of X, the carrier of c₂):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of c₂):],K138( the carrier of X, the carrier of c₂):] is set
RLSStruct(# K138( the carrier of X, the carrier of c₂),(FuncZero ( the carrier of X,c₂)),(FuncAdd ( the carrier of X,c₂)),(FuncExtMult ( the carrier of X,c₂)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,c₂)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,c₂)) is set
Zero_ ((LinearOperators (X,c₂)),(RealVectSpace ( the carrier of X,c₂))) is V15() Function-like Element of LinearOperators (X,c₂)
Add_ ((LinearOperators (X,c₂)),(RealVectSpace ( the carrier of X,c₂))) is V15() Function-like V25([:(LinearOperators (X,c₂)),(LinearOperators (X,c₂)):]) V29([:(LinearOperators (X,c₂)),(LinearOperators (X,c₂)):], LinearOperators (X,c₂)) Element of bool [:[:(LinearOperators (X,c₂)),(LinearOperators (X,c₂)):],(LinearOperators (X,c₂)):]
[:(LinearOperators (X,c₂)),(LinearOperators (X,c₂)):] is V15() set
[:[:(LinearOperators (X,c₂)),(LinearOperators (X,c₂)):],(LinearOperators (X,c₂)):] is V15() set
bool [:[:(LinearOperators (X,c₂)),(LinearOperators (X,c₂)):],(LinearOperators (X,c₂)):] is set
Mult_ ((LinearOperators (X,c₂)),(RealVectSpace ( the carrier of X,c₂))) is V15() Function-like V25([:REAL,(LinearOperators (X,c₂)):]) V29([:REAL,(LinearOperators (X,c₂)):], LinearOperators (X,c₂)) Element of bool [:[:REAL,(LinearOperators (X,c₂)):],(LinearOperators (X,c₂)):]
[:REAL,(LinearOperators (X,c₂)):] is V15() set
[:[:REAL,(LinearOperators (X,c₂)):],(LinearOperators (X,c₂)):] is V15() set
bool [:[:REAL,(LinearOperators (X,c₂)):],(LinearOperators (X,c₂)):] is set
RLSStruct(# (LinearOperators (X,c₂)),(Zero_ ((LinearOperators (X,c₂)),(RealVectSpace ( the carrier of X,c₂)))),(Add_ ((LinearOperators (X,c₂)),(RealVectSpace ( the carrier of X,c₂)))),(Mult_ ((LinearOperators (X,c₂)),(RealVectSpace ( the carrier of X,c₂)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,c₂)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,c₂)) is set
[:(BoundedLinearOperators (X,c₂)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,c₂)),REAL:] is set
BoundedLinearOperatorsNorm (X,UNIT) is non empty V15() Function-like V25( BoundedLinearOperators (X,UNIT)) V29( BoundedLinearOperators (X,UNIT), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,UNIT)),REAL:]
BoundedLinearOperators (X,UNIT) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,UNIT))
R_VectorSpace_of_LinearOperators (X,UNIT) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,UNIT) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,UNIT))
RealVectSpace ( the carrier of X,UNIT) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of UNIT) is non empty functional M4( the carrier of X, the carrier of UNIT)
FuncZero ( the carrier of X,UNIT) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of UNIT) Element of K138( the carrier of X, the carrier of UNIT)
K308( the carrier of UNIT, the carrier of X,(0. UNIT)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of UNIT) Element of bool [: the carrier of X, the carrier of UNIT:]
FuncAdd ( the carrier of X,UNIT) is V15() Function-like V25([:K138( the carrier of X, the carrier of UNIT),K138( the carrier of X, the carrier of UNIT):]) V29([:K138( the carrier of X, the carrier of UNIT),K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT)) Element of bool [:[:K138( the carrier of X, the carrier of UNIT),K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT):]
[:K138( the carrier of X, the carrier of UNIT),K138( the carrier of X, the carrier of UNIT):] is V15() set
[:[:K138( the carrier of X, the carrier of UNIT),K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT):] is V15() set
bool [:[:K138( the carrier of X, the carrier of UNIT),K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT):] is set
FuncExtMult ( the carrier of X,UNIT) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of UNIT):]) V29([:REAL,K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT):]
[:REAL,K138( the carrier of X, the carrier of UNIT):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of UNIT):],K138( the carrier of X, the carrier of UNIT):] is set
RLSStruct(# K138( the carrier of X, the carrier of UNIT),(FuncZero ( the carrier of X,UNIT)),(FuncAdd ( the carrier of X,UNIT)),(FuncExtMult ( the carrier of X,UNIT)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,UNIT)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,UNIT)) is set
Zero_ ((LinearOperators (X,UNIT)),(RealVectSpace ( the carrier of X,UNIT))) is V15() Function-like Element of LinearOperators (X,UNIT)
Add_ ((LinearOperators (X,UNIT)),(RealVectSpace ( the carrier of X,UNIT))) is V15() Function-like V25([:(LinearOperators (X,UNIT)),(LinearOperators (X,UNIT)):]) V29([:(LinearOperators (X,UNIT)),(LinearOperators (X,UNIT)):], LinearOperators (X,UNIT)) Element of bool [:[:(LinearOperators (X,UNIT)),(LinearOperators (X,UNIT)):],(LinearOperators (X,UNIT)):]
[:(LinearOperators (X,UNIT)),(LinearOperators (X,UNIT)):] is V15() set
[:[:(LinearOperators (X,UNIT)),(LinearOperators (X,UNIT)):],(LinearOperators (X,UNIT)):] is V15() set
bool [:[:(LinearOperators (X,UNIT)),(LinearOperators (X,UNIT)):],(LinearOperators (X,UNIT)):] is set
Mult_ ((LinearOperators (X,UNIT)),(RealVectSpace ( the carrier of X,UNIT))) is V15() Function-like V25([:REAL,(LinearOperators (X,UNIT)):]) V29([:REAL,(LinearOperators (X,UNIT)):], LinearOperators (X,UNIT)) Element of bool [:[:REAL,(LinearOperators (X,UNIT)):],(LinearOperators (X,UNIT)):]
[:REAL,(LinearOperators (X,UNIT)):] is V15() set
[:[:REAL,(LinearOperators (X,UNIT)):],(LinearOperators (X,UNIT)):] is V15() set
bool [:[:REAL,(LinearOperators (X,UNIT)):],(LinearOperators (X,UNIT)):] is set
RLSStruct(# (LinearOperators (X,UNIT)),(Zero_ ((LinearOperators (X,UNIT)),(RealVectSpace ( the carrier of X,UNIT)))),(Add_ ((LinearOperators (X,UNIT)),(RealVectSpace ( the carrier of X,UNIT)))),(Mult_ ((LinearOperators (X,UNIT)),(RealVectSpace ( the carrier of X,UNIT)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,UNIT)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,UNIT)) is set
[:(BoundedLinearOperators (X,UNIT)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,UNIT)),REAL:] is set
MULT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of c₂) V165(X,c₂) V166(X,c₂) Lipschitzian Element of bool [: the carrier of X, the carrier of c₂:]
(BoundedLinearOperatorsNorm (X,c₂)) . MULT is V11() real ext-real Element of REAL
ADD is non empty V15() Function-like V25( the carrier of c₂) V29( the carrier of c₂, the carrier of UNIT) V165(c₂,UNIT) V166(c₂,UNIT) Lipschitzian Element of bool [: the carrier of c₂, the carrier of UNIT:]
ADD * MULT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of UNIT) Element of bool [: the carrier of X, the carrier of UNIT:]
(BoundedLinearOperatorsNorm (c₂,UNIT)) . ADD is V11() real ext-real Element of REAL
((BoundedLinearOperatorsNorm (c₂,UNIT)) . ADD) * ((BoundedLinearOperatorsNorm (X,c₂)) . MULT) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,UNIT)) . (ADD * MULT) is V11() real ext-real Element of REAL
R_NormSpace_of_BoundedLinearOperators (X,c₂) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
Zero_ ((BoundedLinearOperators (X,c₂)),(R_VectorSpace_of_LinearOperators (X,c₂))) is Element of BoundedLinearOperators (X,c₂)
Add_ ((BoundedLinearOperators (X,c₂)),(R_VectorSpace_of_LinearOperators (X,c₂))) is V15() Function-like V25([:(BoundedLinearOperators (X,c₂)),(BoundedLinearOperators (X,c₂)):]) V29([:(BoundedLinearOperators (X,c₂)),(BoundedLinearOperators (X,c₂)):], BoundedLinearOperators (X,c₂)) Element of bool [:[:(BoundedLinearOperators (X,c₂)),(BoundedLinearOperators (X,c₂)):],(BoundedLinearOperators (X,c₂)):]
[:(BoundedLinearOperators (X,c₂)),(BoundedLinearOperators (X,c₂)):] is V15() set
[:[:(BoundedLinearOperators (X,c₂)),(BoundedLinearOperators (X,c₂)):],(BoundedLinearOperators (X,c₂)):] is V15() set
bool [:[:(BoundedLinearOperators (X,c₂)),(BoundedLinearOperators (X,c₂)):],(BoundedLinearOperators (X,c₂)):] is set
Mult_ ((BoundedLinearOperators (X,c₂)),(R_VectorSpace_of_LinearOperators (X,c₂))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,c₂)):]) V29([:REAL,(BoundedLinearOperators (X,c₂)):], BoundedLinearOperators (X,c₂)) Element of bool [:[:REAL,(BoundedLinearOperators (X,c₂)):],(BoundedLinearOperators (X,c₂)):]
[:REAL,(BoundedLinearOperators (X,c₂)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,c₂)):],(BoundedLinearOperators (X,c₂)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,c₂)):],(BoundedLinearOperators (X,c₂)):] is set
NORMSTR(# (BoundedLinearOperators (X,c₂)),(Zero_ ((BoundedLinearOperators (X,c₂)),(R_VectorSpace_of_LinearOperators (X,c₂)))),(Add_ ((BoundedLinearOperators (X,c₂)),(R_VectorSpace_of_LinearOperators (X,c₂)))),(Mult_ ((BoundedLinearOperators (X,c₂)),(R_VectorSpace_of_LinearOperators (X,c₂)))),(BoundedLinearOperatorsNorm (X,c₂)) #) is non empty strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂)) is non empty set
R_NormSpace_of_BoundedLinearOperators (c₂,UNIT) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
Zero_ ((BoundedLinearOperators (c₂,UNIT)),(R_VectorSpace_of_LinearOperators (c₂,UNIT))) is Element of BoundedLinearOperators (c₂,UNIT)
Add_ ((BoundedLinearOperators (c₂,UNIT)),(R_VectorSpace_of_LinearOperators (c₂,UNIT))) is V15() Function-like V25([:(BoundedLinearOperators (c₂,UNIT)),(BoundedLinearOperators (c₂,UNIT)):]) V29([:(BoundedLinearOperators (c₂,UNIT)),(BoundedLinearOperators (c₂,UNIT)):], BoundedLinearOperators (c₂,UNIT)) Element of bool [:[:(BoundedLinearOperators (c₂,UNIT)),(BoundedLinearOperators (c₂,UNIT)):],(BoundedLinearOperators (c₂,UNIT)):]
[:(BoundedLinearOperators (c₂,UNIT)),(BoundedLinearOperators (c₂,UNIT)):] is V15() set
[:[:(BoundedLinearOperators (c₂,UNIT)),(BoundedLinearOperators (c₂,UNIT)):],(BoundedLinearOperators (c₂,UNIT)):] is V15() set
bool [:[:(BoundedLinearOperators (c₂,UNIT)),(BoundedLinearOperators (c₂,UNIT)):],(BoundedLinearOperators (c₂,UNIT)):] is set
Mult_ ((BoundedLinearOperators (c₂,UNIT)),(R_VectorSpace_of_LinearOperators (c₂,UNIT))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (c₂,UNIT)):]) V29([:REAL,(BoundedLinearOperators (c₂,UNIT)):], BoundedLinearOperators (c₂,UNIT)) Element of bool [:[:REAL,(BoundedLinearOperators (c₂,UNIT)):],(BoundedLinearOperators (c₂,UNIT)):]
[:REAL,(BoundedLinearOperators (c₂,UNIT)):] is V15() set
[:[:REAL,(BoundedLinearOperators (c₂,UNIT)):],(BoundedLinearOperators (c₂,UNIT)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (c₂,UNIT)):],(BoundedLinearOperators (c₂,UNIT)):] is set
NORMSTR(# (BoundedLinearOperators (c₂,UNIT)),(Zero_ ((BoundedLinearOperators (c₂,UNIT)),(R_VectorSpace_of_LinearOperators (c₂,UNIT)))),(Add_ ((BoundedLinearOperators (c₂,UNIT)),(R_VectorSpace_of_LinearOperators (c₂,UNIT)))),(Mult_ ((BoundedLinearOperators (c₂,UNIT)),(R_VectorSpace_of_LinearOperators (c₂,UNIT)))),(BoundedLinearOperatorsNorm (c₂,UNIT)) #) is non empty strict NORMSTR
the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)) is non empty set
BLOP is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT))
||.BLOP.|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)) is non empty V15() Function-like V25( the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT))) V29( the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)), REAL ) V36() V37() V38() Element of bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)),REAL:]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)),REAL:] is set
the normF of (R_NormSpace_of_BoundedLinearOperators (c₂,UNIT)) . BLOP is V11() real ext-real Element of REAL
RBLOP is left_complementable right_complementable complementable Element of the carrier of X
MULT . RBLOP is left_complementable right_complementable complementable Element of the carrier of c₂
||.(MULT . RBLOP).|| is V11() real ext-real Element of REAL
the normF of c₂ is non empty V15() Function-like V25( the carrier of c₂) V29( the carrier of c₂, REAL ) V36() V37() V38() Element of bool [: the carrier of c₂,REAL:]
[: the carrier of c₂,REAL:] is V15() V36() V37() V38() set
bool [: the carrier of c₂,REAL:] is set
the normF of c₂ . (MULT . RBLOP) is V11() real ext-real Element of REAL
||.BLOP.|| * ||.(MULT . RBLOP).|| is V11() real ext-real Element of REAL
BS is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂))
||.BS.|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,c₂)) is non empty V15() Function-like V25( the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂))) V29( the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂)), REAL ) V36() V37() V38() Element of bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂)),REAL:]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂)),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,c₂)),REAL:] is set
the normF of (R_NormSpace_of_BoundedLinearOperators (X,c₂)) . BS is V11() real ext-real Element of REAL
||.RBLOP.|| is V11() real ext-real Element of REAL
the normF of X is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, REAL ) V36() V37() V38() Element of bool [: the carrier of X,REAL:]
[: the carrier of X,REAL:] is V15() V36() V37() V38() set
bool [: the carrier of X,REAL:] is set
the normF of X . RBLOP is V11() real ext-real Element of REAL
||.BS.|| * ||.RBLOP.|| is V11() real ext-real Element of REAL
||.BLOP.|| * (||.BS.|| * ||.RBLOP.||) is V11() real ext-real Element of REAL
(ADD * MULT) . RBLOP is left_complementable right_complementable complementable Element of the carrier of UNIT
||.((ADD * MULT) . RBLOP).|| is V11() real ext-real Element of REAL
the normF of UNIT is non empty V15() Function-like V25( the carrier of UNIT) V29( the carrier of UNIT, REAL ) V36() V37() V38() Element of bool [: the carrier of UNIT,REAL:]
[: the carrier of UNIT,REAL:] is V15() V36() V37() V38() set
bool [: the carrier of UNIT,REAL:] is set
the normF of UNIT . ((ADD * MULT) . RBLOP) is V11() real ext-real Element of REAL
ADD . (MULT . RBLOP) is left_complementable right_complementable complementable Element of the carrier of UNIT
||.(ADD . (MULT . RBLOP)).|| is V11() real ext-real Element of REAL
the normF of UNIT . (ADD . (MULT . RBLOP)) is V11() real ext-real Element of REAL
||.BLOP.|| * ||.BS.|| is V11() real ext-real Element of REAL
(||.BLOP.|| * ||.BS.||) * ||.RBLOP.|| is V11() real ext-real Element of REAL
seq1 is left_complementable right_complementable complementable Element of the carrier of X
||.seq1.|| is V11() real ext-real Element of REAL
the normF of X . seq1 is V11() real ext-real Element of REAL
(||.BLOP.|| * ||.BS.||) * ||.seq1.|| is V11() real ext-real Element of REAL
(||.BLOP.|| * ||.BS.||) * 1 is V11() real ext-real Element of REAL
(ADD * MULT) . seq1 is left_complementable right_complementable complementable Element of the carrier of UNIT
||.((ADD * MULT) . seq1).|| is V11() real ext-real Element of REAL
the normF of UNIT . ((ADD * MULT) . seq1) is V11() real ext-real Element of REAL
seq1 is V11() real ext-real Element of REAL
RBLOP is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of UNIT) V165(X,UNIT) V166(X,UNIT) Lipschitzian Element of bool [: the carrier of X, the carrier of UNIT:]
PreNorms RBLOP is non empty V51() V52() V53() Element of bool REAL
{ ||.(RBLOP . b₁).|| where b₁ is left_complementable right_complementable complementable Element of the carrier of X : ||.b₁.|| <= 1 } is set
g1 is left_complementable right_complementable complementable Element of the carrier of X
RBLOP . g1 is left_complementable right_complementable complementable Element of the carrier of UNIT
||.(RBLOP . g1).|| is V11() real ext-real Element of REAL
the normF of UNIT . (RBLOP . g1) is V11() real ext-real Element of REAL
||.g1.|| is V11() real ext-real Element of REAL
the normF of X . g1 is V11() real ext-real Element of REAL
upper_bound (PreNorms RBLOP) is V11() real ext-real Element of REAL
seq1 is left_complementable right_complementable complementable Element of the carrier of X
(ADD * MULT) . seq1 is left_complementable right_complementable complementable Element of the carrier of UNIT
||.((ADD * MULT) . seq1).|| is V11() real ext-real Element of REAL
the normF of UNIT . ((ADD * MULT) . seq1) is V11() real ext-real Element of REAL
||.seq1.|| is V11() real ext-real Element of REAL
the normF of X . seq1 is V11() real ext-real Element of REAL
(((BoundedLinearOperatorsNorm (c₂,UNIT)) . ADD) * ((BoundedLinearOperatorsNorm (X,c₂)) . MULT)) * ||.seq1.|| is V11() real ext-real Element of REAL
g1 is V11() real ext-real set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
c₂ is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT * c₂ is V15() Function-like set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
c₂ is Element of BoundedLinearOperators (X,X)
UNIT is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (c₂,UNIT) is Element of BoundedLinearOperators (X,X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
c₂ is Element of BoundedLinearOperators (X,X)
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT is Element of BoundedLinearOperators (X,X)
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
UNIT is V11() real ext-real Element of REAL
c₂ is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (UNIT,c₂) is Element of BoundedLinearOperators (X,X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
c₂ is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
UNIT is Element of BoundedLinearOperators (X,X)
MULT is Element of BoundedLinearOperators (X,X)
c₂ . (UNIT,MULT) is Element of BoundedLinearOperators (X,X)
(X,MULT,UNIT) is Element of BoundedLinearOperators (X,X)
modetrans (MULT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (MULT,X,X)),(modetrans (UNIT,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
c₂ is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
UNIT is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
MULT is Element of BoundedLinearOperators (X,X)
ADD is Element of BoundedLinearOperators (X,X)
c₂ . (MULT,ADD) is Element of BoundedLinearOperators (X,X)
(X,ADD,MULT) is Element of BoundedLinearOperators (X,X)
modetrans (ADD,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (MULT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (ADD,X,X)),(modetrans (MULT,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT . (MULT,ADD) is Element of BoundedLinearOperators (X,X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
c₂ is left_complementable right_complementable complementable Element of the carrier of X
UNIT is left_complementable right_complementable complementable Element of the carrier of X
c₂ + UNIT is left_complementable right_complementable complementable Element of the carrier of X
the addF of X is V15() Function-like V25([: the carrier of X, the carrier of X:]) V29([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[:[: the carrier of X, the carrier of X:], the carrier of X:] is V15() set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the addF of X . (c₂,UNIT) is left_complementable right_complementable complementable Element of the carrier of X
(id the carrier of X) . (c₂ + UNIT) is left_complementable right_complementable complementable Element of the carrier of X
(id the carrier of X) . c₂ is left_complementable right_complementable complementable Element of the carrier of X
((id the carrier of X) . c₂) + UNIT is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((id the carrier of X) . c₂),UNIT) is left_complementable right_complementable complementable Element of the carrier of X
(id the carrier of X) . UNIT is left_complementable right_complementable complementable Element of the carrier of X
((id the carrier of X) . c₂) + ((id the carrier of X) . UNIT) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((id the carrier of X) . c₂),((id the carrier of X) . UNIT)) is left_complementable right_complementable complementable Element of the carrier of X
c₂ is left_complementable right_complementable complementable Element of the carrier of X
UNIT is V11() real ext-real Element of REAL
UNIT * c₂ is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X is V15() Function-like V25([:REAL, the carrier of X:]) V29([:REAL, the carrier of X:], the carrier of X) Element of bool [:[:REAL, the carrier of X:], the carrier of X:]
[:REAL, the carrier of X:] is V15() set
[:[:REAL, the carrier of X:], the carrier of X:] is V15() set
bool [:[:REAL, the carrier of X:], the carrier of X:] is set
the Mult of X . (UNIT,c₂) is set
(id the carrier of X) . (UNIT * c₂) is left_complementable right_complementable complementable Element of the carrier of X
(id the carrier of X) . c₂ is left_complementable right_complementable complementable Element of the carrier of X
UNIT * ((id the carrier of X) . c₂) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X . (UNIT,((id the carrier of X) . c₂)) is set
c₂ is left_complementable right_complementable complementable Element of the carrier of X
(id the carrier of X) . c₂ is left_complementable right_complementable complementable Element of the carrier of X
||.((id the carrier of X) . c₂).|| is V11() real ext-real Element of REAL
the normF of X is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, REAL ) V36() V37() V38() Element of bool [: the carrier of X,REAL:]
[: the carrier of X,REAL:] is V15() V36() V37() V38() set
bool [: the carrier of X,REAL:] is set
the normF of X . ((id the carrier of X) . c₂) is V11() real ext-real Element of REAL
||.c₂.|| is V11() real ext-real Element of REAL
the normF of X . c₂ is V11() real ext-real Element of REAL
1 * ||.c₂.|| is V11() real ext-real Element of REAL
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
MULT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
c₂ is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,UNIT,c₂) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
ADD is left_complementable right_complementable complementable Element of the carrier of X
(X,UNIT,c₂) . ADD is left_complementable right_complementable complementable Element of the carrier of X
UNIT . ADD is left_complementable right_complementable complementable Element of the carrier of X
c₂ . (UNIT . ADD) is left_complementable right_complementable complementable Element of the carrier of X
MULT . ADD is left_complementable right_complementable complementable Element of the carrier of X
ADD is left_complementable right_complementable complementable Element of the carrier of X
MULT . ADD is left_complementable right_complementable complementable Element of the carrier of X
UNIT . ADD is left_complementable right_complementable complementable Element of the carrier of X
c₂ . (UNIT . ADD) is left_complementable right_complementable complementable Element of the carrier of X
BS is left_complementable right_complementable complementable Element of the carrier of X
MULT . BS is left_complementable right_complementable complementable Element of the carrier of X
UNIT . BS is left_complementable right_complementable complementable Element of the carrier of X
c₂ . (UNIT . BS) is left_complementable right_complementable complementable Element of the carrier of X
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
MULT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,MULT,UNIT) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
c₂ is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,MULT,UNIT),c₂) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,UNIT,c₂) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,MULT,(X,UNIT,c₂)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
ADD is left_complementable right_complementable complementable Element of the carrier of X
(X,(X,MULT,UNIT),c₂) . ADD is left_complementable right_complementable complementable Element of the carrier of X
(X,MULT,UNIT) . ADD is left_complementable right_complementable complementable Element of the carrier of X
c₂ . ((X,MULT,UNIT) . ADD) is left_complementable right_complementable complementable Element of the carrier of X
MULT . ADD is left_complementable right_complementable complementable Element of the carrier of X
UNIT . (MULT . ADD) is left_complementable right_complementable complementable Element of the carrier of X
c₂ . (UNIT . (MULT . ADD)) is left_complementable right_complementable complementable Element of the carrier of X
(X,UNIT,c₂) . (MULT . ADD) is left_complementable right_complementable complementable Element of the carrier of X
(X,MULT,(X,UNIT,c₂)) . ADD is left_complementable right_complementable complementable Element of the carrier of X
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty set
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
UNIT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
UNIT * (id the carrier of X) is non empty V15() V18( the carrier of X) Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
(id the carrier of X) * UNIT is non empty V15() V19( the carrier of X) Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
MULT is left_complementable right_complementable complementable Element of the carrier of X
((id the carrier of X) * UNIT) . MULT is left_complementable right_complementable complementable Element of the carrier of X
c₂ is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,UNIT,c₂) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,UNIT,c₂) . MULT is left_complementable right_complementable complementable Element of the carrier of X
UNIT . MULT is left_complementable right_complementable complementable Element of the carrier of X
c₂ . (UNIT . MULT) is left_complementable right_complementable complementable Element of the carrier of X
MULT is left_complementable right_complementable complementable Element of the carrier of X
(UNIT * (id the carrier of X)) . MULT is left_complementable right_complementable complementable Element of the carrier of X
(X,c₂,UNIT) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,c₂,UNIT) . MULT is left_complementable right_complementable complementable Element of the carrier of X
c₂ . MULT is left_complementable right_complementable complementable Element of the carrier of X
UNIT . (c₂ . MULT) is left_complementable right_complementable complementable Element of the carrier of X
UNIT . MULT is left_complementable right_complementable complementable Element of the carrier of X
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
MULT is Element of BoundedLinearOperators (X,X)
UNIT is Element of BoundedLinearOperators (X,X)
(X,MULT,UNIT) is Element of BoundedLinearOperators (X,X)
modetrans (MULT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (MULT,X,X)),(modetrans (UNIT,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
c₂ is Element of BoundedLinearOperators (X,X)
(X,(X,MULT,UNIT),c₂) is Element of BoundedLinearOperators (X,X)
modetrans ((X,MULT,UNIT),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,MULT,UNIT),X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,UNIT,c₂) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,MULT,(X,UNIT,c₂)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,UNIT,c₂),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (MULT,X,X)),(modetrans ((X,UNIT,c₂),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (MULT,X,X)),(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X)))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
c₂ is Element of BoundedLinearOperators (X,X)
(X,(X),c₂) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,c₂,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (c₂,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((id the carrier of X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
UNIT is Element of BoundedLinearOperators (X,X)
MULT is Element of BoundedLinearOperators (X,X)
(X,UNIT,MULT) is Element of BoundedLinearOperators (X,X)
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (UNIT,MULT) is Element of BoundedLinearOperators (X,X)
c₂ is Element of BoundedLinearOperators (X,X)
(X,(X,UNIT,MULT),c₂) is Element of BoundedLinearOperators (X,X)
modetrans ((X,UNIT,MULT),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,UNIT,MULT),X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,UNIT,c₂) is Element of BoundedLinearOperators (X,X)
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,MULT,c₂) is Element of BoundedLinearOperators (X,X)
modetrans (MULT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (MULT,X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,UNIT,c₂),(X,MULT,c₂)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,UNIT,c₂),(X,MULT,c₂)) is Element of BoundedLinearOperators (X,X)
R_NormSpace_of_BoundedLinearOperators (X,X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
NORMSTR(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X)) #) is non empty strict NORMSTR
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))),(X,(modetrans (MULT,X,X)),(modetrans (c₂,X,X)))) is set
the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty set
n is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans ((X,UNIT,MULT),X,X)),(modetrans (c₂,X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans (MULT,X,X)),(modetrans (c₂,X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g) + ((X,(modetrans (MULT,X,X)),(modetrans (c₂,X,X))) . g) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X is V15() Function-like V25([: the carrier of X, the carrier of X:]) V29([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[:[: the carrier of X, the carrier of X:], the carrier of X:] is V15() set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the addF of X . (((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g),((X,(modetrans (MULT,X,X)),(modetrans (c₂,X,X))) . g)) is left_complementable right_complementable complementable Element of the carrier of X
n + m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (n,m) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(modetrans ((X,UNIT,MULT),X,X)) . g is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (UNIT,X,X)) . g is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (MULT,X,X)) . g is left_complementable right_complementable complementable Element of the carrier of X
((modetrans (UNIT,X,X)) . g) + ((modetrans (MULT,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((modetrans (UNIT,X,X)) . g),((modetrans (MULT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (c₂,X,X)) . ((modetrans ((X,UNIT,MULT),X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (c₂,X,X)) . ((modetrans (MULT,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g)) + ((modetrans (c₂,X,X)) . ((modetrans (MULT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g)),((modetrans (c₂,X,X)) . ((modetrans (MULT,X,X)) . g))) is left_complementable right_complementable complementable Element of the carrier of X
((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g) + ((modetrans (c₂,X,X)) . ((modetrans (MULT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g),((modetrans (c₂,X,X)) . ((modetrans (MULT,X,X)) . g))) is left_complementable right_complementable complementable Element of the carrier of X
r is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g + g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (g,g1) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
c₂ is Element of BoundedLinearOperators (X,X)
UNIT is Element of BoundedLinearOperators (X,X)
MULT is Element of BoundedLinearOperators (X,X)
(X,UNIT,MULT) is Element of BoundedLinearOperators (X,X)
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (UNIT,MULT) is Element of BoundedLinearOperators (X,X)
(X,c₂,(X,UNIT,MULT)) is Element of BoundedLinearOperators (X,X)
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,UNIT,MULT),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (c₂,X,X)),(modetrans ((X,UNIT,MULT),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,c₂,UNIT) is Element of BoundedLinearOperators (X,X)
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,c₂,MULT) is Element of BoundedLinearOperators (X,X)
modetrans (MULT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (c₂,X,X)),(modetrans (MULT,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,c₂,UNIT),(X,c₂,MULT)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,c₂,UNIT),(X,c₂,MULT)) is Element of BoundedLinearOperators (X,X)
R_NormSpace_of_BoundedLinearOperators (X,X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
NORMSTR(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X)) #) is non empty strict NORMSTR
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))),(X,(modetrans (c₂,X,X)),(modetrans (MULT,X,X)))) is set
the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty set
n is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans (c₂,X,X)),(modetrans ((X,UNIT,MULT),X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans (c₂,X,X)),(modetrans (MULT,X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
((X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) . g) + ((X,(modetrans (c₂,X,X)),(modetrans (MULT,X,X))) . g) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X is V15() Function-like V25([: the carrier of X, the carrier of X:]) V29([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[:[: the carrier of X, the carrier of X:], the carrier of X:] is V15() set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is set
the addF of X . (((X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) . g),((X,(modetrans (c₂,X,X)),(modetrans (MULT,X,X))) . g)) is left_complementable right_complementable complementable Element of the carrier of X
n + m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (n,m) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(modetrans (c₂,X,X)) . g is left_complementable right_complementable complementable Element of the carrier of X
(modetrans ((X,UNIT,MULT),X,X)) . ((modetrans (c₂,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (UNIT,X,X)) . ((modetrans (c₂,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (MULT,X,X)) . ((modetrans (c₂,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
((modetrans (UNIT,X,X)) . ((modetrans (c₂,X,X)) . g)) + ((modetrans (MULT,X,X)) . ((modetrans (c₂,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((modetrans (UNIT,X,X)) . ((modetrans (c₂,X,X)) . g)),((modetrans (MULT,X,X)) . ((modetrans (c₂,X,X)) . g))) is left_complementable right_complementable complementable Element of the carrier of X
((X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) . g) + ((modetrans (MULT,X,X)) . ((modetrans (c₂,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
the addF of X . (((X,(modetrans (c₂,X,X)),(modetrans (UNIT,X,X))) . g),((modetrans (MULT,X,X)) . ((modetrans (c₂,X,X)) . g))) is left_complementable right_complementable complementable Element of the carrier of X
r is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g + g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (g,g1) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
UNIT is Element of BoundedLinearOperators (X,X)
c₂ is Element of BoundedLinearOperators (X,X)
(X,UNIT,c₂) is Element of BoundedLinearOperators (X,X)
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
MULT is V11() real ext-real Element of REAL
ADD is V11() real ext-real Element of REAL
MULT * ADD is V11() real ext-real Element of REAL
(X,(X,UNIT,c₂),(MULT * ADD)) is Element of BoundedLinearOperators (X,X)
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((MULT * ADD),(X,UNIT,c₂)) is Element of BoundedLinearOperators (X,X)
(X,UNIT,ADD) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (ADD,UNIT) is Element of BoundedLinearOperators (X,X)
(X,c₂,MULT) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (MULT,c₂) is Element of BoundedLinearOperators (X,X)
(X,(X,UNIT,ADD),(X,c₂,MULT)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,UNIT,ADD),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,c₂,MULT),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,UNIT,ADD),X,X)),(modetrans ((X,c₂,MULT),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
R_NormSpace_of_BoundedLinearOperators (X,X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
NORMSTR(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X)) #) is non empty strict NORMSTR
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((MULT * ADD),(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X)))) is set
the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty set
n is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans ((X,UNIT,ADD),X,X)),(modetrans ((X,c₂,MULT),X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g is left_complementable right_complementable complementable Element of the carrier of X
(MULT * ADD) * ((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X is V15() Function-like V25([:REAL, the carrier of X:]) V29([:REAL, the carrier of X:], the carrier of X) Element of bool [:[:REAL, the carrier of X:], the carrier of X:]
[:REAL, the carrier of X:] is V15() set
[:[:REAL, the carrier of X:], the carrier of X:] is V15() set
bool [:[:REAL, the carrier of X:], the carrier of X:] is set
the Mult of X . ((MULT * ADD),((X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) . g)) is set
(modetrans (UNIT,X,X)) . g is left_complementable right_complementable complementable Element of the carrier of X
ADD * ((modetrans (UNIT,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X . (ADD,((modetrans (UNIT,X,X)) . g)) is set
MULT * m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (MULT,m) is set
(modetrans ((X,c₂,MULT),X,X)) . (ADD * ((modetrans (UNIT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (c₂,X,X)) . (ADD * ((modetrans (UNIT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
MULT * ((modetrans (c₂,X,X)) . (ADD * ((modetrans (UNIT,X,X)) . g))) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X . (MULT,((modetrans (c₂,X,X)) . (ADD * ((modetrans (UNIT,X,X)) . g)))) is set
ADD * n is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (ADD,n) is set
(modetrans ((X,UNIT,ADD),X,X)) . g is left_complementable right_complementable complementable Element of the carrier of X
(modetrans ((X,c₂,MULT),X,X)) . ((modetrans ((X,UNIT,ADD),X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
(modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g) is left_complementable right_complementable complementable Element of the carrier of X
ADD * ((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X . (ADD,((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g))) is set
MULT * (ADD * ((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g))) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X . (MULT,(ADD * ((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g)))) is set
(MULT * ADD) * ((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g)) is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X . ((MULT * ADD),((modetrans (c₂,X,X)) . ((modetrans (UNIT,X,X)) . g))) is set
g is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
r is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(MULT * ADD) * r is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((MULT * ADD),r) is set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
UNIT is Element of BoundedLinearOperators (X,X)
c₂ is Element of BoundedLinearOperators (X,X)
(X,UNIT,c₂) is Element of BoundedLinearOperators (X,X)
modetrans (UNIT,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (c₂,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (UNIT,X,X)),(modetrans (c₂,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
MULT is V11() real ext-real Element of REAL
(X,(X,UNIT,c₂),MULT) is Element of BoundedLinearOperators (X,X)
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (MULT,(X,UNIT,c₂)) is Element of BoundedLinearOperators (X,X)
(X,c₂,MULT) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (MULT,c₂) is Element of BoundedLinearOperators (X,X)
(X,UNIT,(X,c₂,MULT)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,c₂,MULT),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (UNIT,X,X)),(modetrans ((X,c₂,MULT),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
(X,UNIT,1) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (1,UNIT) is Element of BoundedLinearOperators (X,X)
BS is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
1 * BS is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (1,BS) is set
MULT * 1 is V11() real ext-real Element of REAL
(X,(X,UNIT,c₂),(MULT * 1)) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((MULT * 1),(X,UNIT,c₂)) is Element of BoundedLinearOperators (X,X)
(X,(X,UNIT,1),(X,c₂,MULT)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,UNIT,1),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,UNIT,1),X,X)),(modetrans ((X,c₂,MULT),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
the carrier of (X) is non empty set
UNIT is Element of the carrier of (X)
MULT is Element of the carrier of (X)
UNIT * MULT is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (UNIT,MULT) is Element of the carrier of (X)
ADD is Element of BoundedLinearOperators (X,X)
(X,(X),ADD) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (ADD,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (ADD,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
MULT * UNIT is Element of the carrier of (X)
the multF of (X) . (MULT,UNIT) is Element of the carrier of (X)
(X,ADD,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (ADD,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
the carrier of (X) is non empty set
c₂ is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
UNIT * c₂ is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT is Element of the carrier of (X)
c₂ * MULT is Element of the carrier of (X)
the multF of (X) . (c₂,MULT) is Element of the carrier of (X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict unital doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
the carrier of (X) is non empty set
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
1. (X) is Element of the carrier of (X)
the OneF of (X) is Element of the carrier of (X)
c₂ is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
c₂ + UNIT is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (c₂,UNIT) is Element of the carrier of (X)
UNIT + c₂ is Element of the carrier of (X)
the addF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT is Element of the carrier of (X)
(c₂ + UNIT) + MULT is Element of the carrier of (X)
the addF of (X) . ((c₂ + UNIT),MULT) is Element of the carrier of (X)
UNIT + MULT is Element of the carrier of (X)
the addF of (X) . (UNIT,MULT) is Element of the carrier of (X)
c₂ + (UNIT + MULT) is Element of the carrier of (X)
the addF of (X) . (c₂,(UNIT + MULT)) is Element of the carrier of (X)
c₂ + (0. (X)) is Element of the carrier of (X)
the addF of (X) . (c₂,(0. (X))) is Element of the carrier of (X)
c₂ * UNIT is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . (c₂,UNIT) is Element of the carrier of (X)
(c₂ * UNIT) * MULT is Element of the carrier of (X)
the multF of (X) . ((c₂ * UNIT),MULT) is Element of the carrier of (X)
UNIT * MULT is Element of the carrier of (X)
the multF of (X) . (UNIT,MULT) is Element of the carrier of (X)
c₂ * (UNIT * MULT) is Element of the carrier of (X)
the multF of (X) . (c₂,(UNIT * MULT)) is Element of the carrier of (X)
c₂ * (1. (X)) is Element of the carrier of (X)
the multF of (X) . (c₂,(1. (X))) is Element of the carrier of (X)
(1. (X)) * c₂ is Element of the carrier of (X)
the multF of (X) . ((1. (X)),c₂) is Element of the carrier of (X)
c₂ * (UNIT + MULT) is Element of the carrier of (X)
the multF of (X) . (c₂,(UNIT + MULT)) is Element of the carrier of (X)
c₂ * MULT is Element of the carrier of (X)
the multF of (X) . (c₂,MULT) is Element of the carrier of (X)
(c₂ * UNIT) + (c₂ * MULT) is Element of the carrier of (X)
the addF of (X) . ((c₂ * UNIT),(c₂ * MULT)) is Element of the carrier of (X)
(UNIT + MULT) * c₂ is Element of the carrier of (X)
the multF of (X) . ((UNIT + MULT),c₂) is Element of the carrier of (X)
UNIT * c₂ is Element of the carrier of (X)
the multF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT * c₂ is Element of the carrier of (X)
the multF of (X) . (MULT,c₂) is Element of the carrier of (X)
(UNIT * c₂) + (MULT * c₂) is Element of the carrier of (X)
the addF of (X) . ((UNIT * c₂),(MULT * c₂)) is Element of the carrier of (X)
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(g1 + g) + r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((g1 + g),r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g + r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g,r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + (g + r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,(g + r)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V80( RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the ZeroF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + (0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,(0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #))) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
m is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + m is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,m) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
n is Element of the carrier of (X)
c₂ + n is Element of the carrier of (X)
the addF of (X) . (c₂,n) is Element of the carrier of (X)
n is Element of BoundedLinearOperators (X,X)
m is Element of BoundedLinearOperators (X,X)
(X,n,m) is Element of BoundedLinearOperators (X,X)
modetrans (n,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (m,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (n,X,X)),(modetrans (m,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
g is Element of BoundedLinearOperators (X,X)
(X) . ((X,n,m),g) is Element of BoundedLinearOperators (X,X)
(X,g,(X,n,m)) is Element of BoundedLinearOperators (X,X)
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,n,m),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans ((X,n,m),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,n) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans (n,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,g,n),m) is Element of BoundedLinearOperators (X,X)
modetrans ((X,g,n),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,g,n),X,X)),(modetrans (m,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X) . (m,(X,g,n)) is Element of BoundedLinearOperators (X,X)
(X,(X),m) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (m,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,m,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (m,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,n,g) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (n,g) is Element of BoundedLinearOperators (X,X)
(X,(X,n,g),m) is Element of BoundedLinearOperators (X,X)
modetrans ((X,n,g),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,n,g),X,X)),(modetrans (m,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,m) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans (m,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,n,m),(X,g,m)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,n,m),(X,g,m)) is Element of BoundedLinearOperators (X,X)
(X) . (m,g) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,n,m),((X) . (m,g))) is Element of BoundedLinearOperators (X,X)
(X,m,(X,n,g)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (m,X,X)),(modetrans ((X,n,g),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,m,n) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (m,X,X)),(modetrans (n,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,m,g) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (m,X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,m,n),(X,m,g)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,m,n),(X,m,g)) is Element of BoundedLinearOperators (X,X)
(X) . (g,m) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,m,n),((X) . (g,m))) is Element of BoundedLinearOperators (X,X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict unital doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
the carrier of (X) is non empty set
UNIT is Element of the carrier of (X)
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
the carrier of (X) is non empty set
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
1. (X) is Element of the carrier of (X)
the OneF of (X) is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
MULT is Element of the carrier of (X)
UNIT + MULT is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (UNIT,MULT) is Element of the carrier of (X)
MULT + UNIT is Element of the carrier of (X)
the addF of (X) . (MULT,UNIT) is Element of the carrier of (X)
ADD is Element of the carrier of (X)
BS is Element of the carrier of (X)
ADD + BS is Element of the carrier of (X)
the addF of (X) . (ADD,BS) is Element of the carrier of (X)
BLOP is Element of the carrier of (X)
(ADD + BS) + BLOP is Element of the carrier of (X)
the addF of (X) . ((ADD + BS),BLOP) is Element of the carrier of (X)
BS + BLOP is Element of the carrier of (X)
the addF of (X) . (BS,BLOP) is Element of the carrier of (X)
ADD + (BS + BLOP) is Element of the carrier of (X)
the addF of (X) . (ADD,(BS + BLOP)) is Element of the carrier of (X)
RBLOP is Element of the carrier of (X)
RBLOP + (0. (X)) is Element of the carrier of (X)
the addF of (X) . (RBLOP,(0. (X))) is Element of the carrier of (X)
seq is Element of the carrier of (X)
seq1 is Element of the carrier of (X)
g1 is Element of the carrier of (X)
seq1 * g1 is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . (seq1,g1) is Element of the carrier of (X)
g is Element of the carrier of (X)
(seq1 * g1) * g is Element of the carrier of (X)
the multF of (X) . ((seq1 * g1),g) is Element of the carrier of (X)
g1 * g is Element of the carrier of (X)
the multF of (X) . (g1,g) is Element of the carrier of (X)
seq1 * (g1 * g) is Element of the carrier of (X)
the multF of (X) . (seq1,(g1 * g)) is Element of the carrier of (X)
r is Element of the carrier of (X)
r * (1. (X)) is Element of the carrier of (X)
the multF of (X) . (r,(1. (X))) is Element of the carrier of (X)
m is Element of the carrier of (X)
(1. (X)) * m is Element of the carrier of (X)
the multF of (X) . ((1. (X)),m) is Element of the carrier of (X)
n is Element of the carrier of (X)
g is Element of the carrier of (X)
h is Element of the carrier of (X)
g + h is Element of the carrier of (X)
the addF of (X) . (g,h) is Element of the carrier of (X)
n * (g + h) is Element of the carrier of (X)
the multF of (X) . (n,(g + h)) is Element of the carrier of (X)
n * g is Element of the carrier of (X)
the multF of (X) . (n,g) is Element of the carrier of (X)
n * h is Element of the carrier of (X)
the multF of (X) . (n,h) is Element of the carrier of (X)
(n * g) + (n * h) is Element of the carrier of (X)
the addF of (X) . ((n * g),(n * h)) is Element of the carrier of (X)
yy is Element of the carrier of (X)
zz is Element of the carrier of (X)
yy + zz is Element of the carrier of (X)
the addF of (X) . (yy,zz) is Element of the carrier of (X)
xx is Element of the carrier of (X)
(yy + zz) * xx is Element of the carrier of (X)
the multF of (X) . ((yy + zz),xx) is Element of the carrier of (X)
yy * xx is Element of the carrier of (X)
the multF of (X) . (yy,xx) is Element of the carrier of (X)
zz * xx is Element of the carrier of (X)
the multF of (X) . (zz,xx) is Element of the carrier of (X)
(yy * xx) + (zz * xx) is Element of the carrier of (X)
the addF of (X) . ((yy * xx),(zz * xx)) is Element of the carrier of (X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict unital doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
the carrier of (X) is non empty set
UNIT is Element of the carrier of (X)
MULT is Element of the carrier of (X)
UNIT * MULT is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (UNIT,MULT) is Element of the carrier of (X)
ADD is Element of BoundedLinearOperators (X,X)
(X,(X),ADD) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (ADD,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (ADD,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
MULT * UNIT is Element of the carrier of (X)
the multF of (X) . (MULT,UNIT) is Element of the carrier of (X)
(X,ADD,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (ADD,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
the carrier of (X) is non empty set
c₂ is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
UNIT * c₂ is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT is Element of the carrier of (X)
c₂ * MULT is Element of the carrier of (X)
the multF of (X) . (c₂,MULT) is Element of the carrier of (X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict unital AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
the carrier of (X) is non empty set
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
1. (X) is Element of the carrier of (X)
the OneF of (X) is Element of the carrier of (X)
c₂ is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
c₂ + UNIT is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (c₂,UNIT) is Element of the carrier of (X)
UNIT + c₂ is Element of the carrier of (X)
the addF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT is Element of the carrier of (X)
(c₂ + UNIT) + MULT is Element of the carrier of (X)
the addF of (X) . ((c₂ + UNIT),MULT) is Element of the carrier of (X)
UNIT + MULT is Element of the carrier of (X)
the addF of (X) . (UNIT,MULT) is Element of the carrier of (X)
c₂ + (UNIT + MULT) is Element of the carrier of (X)
the addF of (X) . (c₂,(UNIT + MULT)) is Element of the carrier of (X)
c₂ + (0. (X)) is Element of the carrier of (X)
the addF of (X) . (c₂,(0. (X))) is Element of the carrier of (X)
c₂ * UNIT is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . (c₂,UNIT) is Element of the carrier of (X)
(c₂ * UNIT) * MULT is Element of the carrier of (X)
the multF of (X) . ((c₂ * UNIT),MULT) is Element of the carrier of (X)
UNIT * MULT is Element of the carrier of (X)
the multF of (X) . (UNIT,MULT) is Element of the carrier of (X)
c₂ * (UNIT * MULT) is Element of the carrier of (X)
the multF of (X) . (c₂,(UNIT * MULT)) is Element of the carrier of (X)
c₂ * (1. (X)) is Element of the carrier of (X)
the multF of (X) . (c₂,(1. (X))) is Element of the carrier of (X)
(1. (X)) * c₂ is Element of the carrier of (X)
the multF of (X) . ((1. (X)),c₂) is Element of the carrier of (X)
c₂ * (UNIT + MULT) is Element of the carrier of (X)
the multF of (X) . (c₂,(UNIT + MULT)) is Element of the carrier of (X)
c₂ * MULT is Element of the carrier of (X)
the multF of (X) . (c₂,MULT) is Element of the carrier of (X)
(c₂ * UNIT) + (c₂ * MULT) is Element of the carrier of (X)
the addF of (X) . ((c₂ * UNIT),(c₂ * MULT)) is Element of the carrier of (X)
(UNIT + MULT) * c₂ is Element of the carrier of (X)
the multF of (X) . ((UNIT + MULT),c₂) is Element of the carrier of (X)
UNIT * c₂ is Element of the carrier of (X)
the multF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT * c₂ is Element of the carrier of (X)
the multF of (X) . (MULT,c₂) is Element of the carrier of (X)
(UNIT * c₂) + (MULT * c₂) is Element of the carrier of (X)
the addF of (X) . ((UNIT * c₂),(MULT * c₂)) is Element of the carrier of (X)
ADD is V11() real ext-real Element of REAL
ADD * (c₂ * UNIT) is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . (ADD,(c₂ * UNIT)) is set
ADD * c₂ is Element of the carrier of (X)
the Mult of (X) . (ADD,c₂) is set
(ADD * c₂) * UNIT is Element of the carrier of (X)
the multF of (X) . ((ADD * c₂),UNIT) is Element of the carrier of (X)
ADD * (c₂ + UNIT) is Element of the carrier of (X)
the Mult of (X) . (ADD,(c₂ + UNIT)) is set
ADD * UNIT is Element of the carrier of (X)
the Mult of (X) . (ADD,UNIT) is set
(ADD * c₂) + (ADD * UNIT) is Element of the carrier of (X)
the addF of (X) . ((ADD * c₂),(ADD * UNIT)) is Element of the carrier of (X)
BS is V11() real ext-real Element of REAL
ADD + BS is V11() real ext-real Element of REAL
(ADD + BS) * c₂ is Element of the carrier of (X)
the Mult of (X) . ((ADD + BS),c₂) is set
BS * c₂ is Element of the carrier of (X)
the Mult of (X) . (BS,c₂) is set
(ADD * c₂) + (BS * c₂) is Element of the carrier of (X)
the addF of (X) . ((ADD * c₂),(BS * c₂)) is Element of the carrier of (X)
ADD * BS is V11() real ext-real Element of REAL
(ADD * BS) * c₂ is Element of the carrier of (X)
the Mult of (X) . ((ADD * BS),c₂) is set
ADD * (BS * c₂) is Element of the carrier of (X)
the Mult of (X) . (ADD,(BS * c₂)) is set
(ADD * BS) * (c₂ * UNIT) is Element of the carrier of (X)
the Mult of (X) . ((ADD * BS),(c₂ * UNIT)) is set
BS * UNIT is Element of the carrier of (X)
the Mult of (X) . (BS,UNIT) is set
(ADD * c₂) * (BS * UNIT) is Element of the carrier of (X)
the multF of (X) . ((ADD * c₂),(BS * UNIT)) is Element of the carrier of (X)
RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
m is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
r + m is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (r,m) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(r + m) + n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((r + m),n) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
m + n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (m,n) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
r + (m + n) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (r,(m + n)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V80( RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the ZeroF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
r + (0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (r,(0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #))) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
r + g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (r,g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
h is Element of the carrier of (X)
c₂ + h is Element of the carrier of (X)
the addF of (X) . (c₂,h) is Element of the carrier of (X)
h is Element of BoundedLinearOperators (X,X)
g is Element of BoundedLinearOperators (X,X)
(X,h,g) is Element of BoundedLinearOperators (X,X)
modetrans (h,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (h,X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
xx is Element of BoundedLinearOperators (X,X)
(X) . ((X,h,g),xx) is Element of BoundedLinearOperators (X,X)
(X,xx,(X,h,g)) is Element of BoundedLinearOperators (X,X)
modetrans (xx,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,h,g),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (xx,X,X)),(modetrans ((X,h,g),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,xx,h) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (xx,X,X)),(modetrans (h,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,xx,h),g) is Element of BoundedLinearOperators (X,X)
modetrans ((X,xx,h),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,xx,h),X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X) . (g,(X,xx,h)) is Element of BoundedLinearOperators (X,X)
(X,(X),g) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,h,xx) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (h,xx) is Element of BoundedLinearOperators (X,X)
(X,(X,h,xx),g) is Element of BoundedLinearOperators (X,X)
modetrans ((X,h,xx),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,h,xx),X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,xx,g) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (xx,X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,h,g),(X,xx,g)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,h,g),(X,xx,g)) is Element of BoundedLinearOperators (X,X)
(X) . (g,xx) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,h,g),((X) . (g,xx))) is Element of BoundedLinearOperators (X,X)
(X,g,(X,h,xx)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans ((X,h,xx),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,h) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans (h,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,xx) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans (xx,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,g,h),(X,g,xx)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,g,h),(X,g,xx)) is Element of BoundedLinearOperators (X,X)
(X) . (xx,g) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,g,h),((X) . (xx,g))) is Element of BoundedLinearOperators (X,X)
(X,(X,h,g),ADD) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (ADD,(X,h,g)) is Element of BoundedLinearOperators (X,X)
(X,g,ADD) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (ADD,g) is Element of BoundedLinearOperators (X,X)
(X,h,(X,g,ADD)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,g,ADD),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (h,X,X)),(modetrans ((X,g,ADD),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
ADD * (r + m) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,(r + m)) is set
ADD * r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,r) is set
ADD * m is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,m) is set
(ADD * r) + (ADD * m) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD * r),(ADD * m)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(ADD + BS) * r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD + BS),r) is set
BS * r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (BS,r) is set
(ADD * r) + (BS * r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD * r),(BS * r)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(ADD * BS) * r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD * BS),r) is set
ADD * (BS * r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,(BS * r)) is set
(X,(X,h,g),(ADD * BS)) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((ADD * BS),(X,h,g)) is Element of BoundedLinearOperators (X,X)
(X,h,BS) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (BS,h) is Element of BoundedLinearOperators (X,X)
(X,(X,h,BS),(X,g,ADD)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,h,BS),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,h,BS),X,X)),(modetrans ((X,g,ADD),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty strict unital AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
seq is Element of the carrier of (X)
RBLOP + seq is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (RBLOP,seq) is Element of the carrier of (X)
seq + RBLOP is Element of the carrier of (X)
the addF of (X) . (seq,RBLOP) is Element of the carrier of (X)
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
seq1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
seq1 + g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (seq1,g1) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
seq is Element of the carrier of (X)
RBLOP + seq is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (RBLOP,seq) is Element of the carrier of (X)
seq1 is Element of the carrier of (X)
(RBLOP + seq) + seq1 is Element of the carrier of (X)
the addF of (X) . ((RBLOP + seq),seq1) is Element of the carrier of (X)
seq + seq1 is Element of the carrier of (X)
the addF of (X) . (seq,seq1) is Element of the carrier of (X)
RBLOP + (seq + seq1) is Element of the carrier of (X)
the addF of (X) . (RBLOP,(seq + seq1)) is Element of the carrier of (X)
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(g1 + g) + r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((g1 + g),r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g + r is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g,r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + (g + r) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,(g + r)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
RBLOP + (0. (X)) is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (RBLOP,(0. (X))) is Element of the carrier of (X)
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
seq is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V80( RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the ZeroF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
seq + (0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (seq,(0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #))) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
seq is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V80( RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the ZeroF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
seq1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
seq + seq1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (seq,seq1) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 is Element of the carrier of (X)
RBLOP + g1 is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (RBLOP,g1) is Element of the carrier of (X)
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
seq is Element of the carrier of (X)
RBLOP * seq is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (RBLOP,seq) is Element of the carrier of (X)
seq1 is Element of the carrier of (X)
(RBLOP * seq) * seq1 is Element of the carrier of (X)
the multF of (X) . ((RBLOP * seq),seq1) is Element of the carrier of (X)
seq * seq1 is Element of the carrier of (X)
the multF of (X) . (seq,seq1) is Element of the carrier of (X)
RBLOP * (seq * seq1) is Element of the carrier of (X)
the multF of (X) . (RBLOP,(seq * seq1)) is Element of the carrier of (X)
g is Element of BoundedLinearOperators (X,X)
g1 is Element of BoundedLinearOperators (X,X)
(X,g,g1) is Element of BoundedLinearOperators (X,X)
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (g1,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
r is Element of BoundedLinearOperators (X,X)
(X) . ((X,g,g1),r) is Element of BoundedLinearOperators (X,X)
(X,r,(X,g,g1)) is Element of BoundedLinearOperators (X,X)
modetrans (r,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,g,g1),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (r,X,X)),(modetrans ((X,g,g1),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,r,g) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (r,X,X)),(modetrans (g,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,r,g),g1) is Element of BoundedLinearOperators (X,X)
modetrans ((X,r,g),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,r,g),X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X) . (g1,(X,r,g)) is Element of BoundedLinearOperators (X,X)
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
1. (X) is Element of the carrier of (X)
the OneF of (X) is Element of the carrier of (X)
RBLOP * (1. (X)) is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (RBLOP,(1. (X))) is Element of the carrier of (X)
seq is Element of BoundedLinearOperators (X,X)
(X,(X),seq) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (seq,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (seq,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
seq is Element of the carrier of (X)
seq1 is Element of the carrier of (X)
seq + seq1 is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (seq,seq1) is Element of the carrier of (X)
RBLOP * (seq + seq1) is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . (RBLOP,(seq + seq1)) is Element of the carrier of (X)
RBLOP * seq is Element of the carrier of (X)
the multF of (X) . (RBLOP,seq) is Element of the carrier of (X)
RBLOP * seq1 is Element of the carrier of (X)
the multF of (X) . (RBLOP,seq1) is Element of the carrier of (X)
(RBLOP * seq) + (RBLOP * seq1) is Element of the carrier of (X)
the addF of (X) . ((RBLOP * seq),(RBLOP * seq1)) is Element of the carrier of (X)
g is Element of BoundedLinearOperators (X,X)
r is Element of BoundedLinearOperators (X,X)
(X,g,r) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (g,r) is Element of BoundedLinearOperators (X,X)
g1 is Element of BoundedLinearOperators (X,X)
(X,(X,g,r),g1) is Element of BoundedLinearOperators (X,X)
modetrans ((X,g,r),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (g1,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,g,r),X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,g1) is Element of BoundedLinearOperators (X,X)
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,r,g1) is Element of BoundedLinearOperators (X,X)
modetrans (r,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (r,X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,g,g1),(X,r,g1)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,g,g1),(X,r,g1)) is Element of BoundedLinearOperators (X,X)
(X) . (g1,r) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,g,g1),((X) . (g1,r))) is Element of BoundedLinearOperators (X,X)
the carrier of (X) is non empty set
RBLOP is V11() real ext-real set
seq is Element of the carrier of (X)
seq1 is Element of the carrier of (X)
seq + seq1 is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (seq,seq1) is Element of the carrier of (X)
RBLOP * (seq + seq1) is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . (RBLOP,(seq + seq1)) is set
RBLOP * seq is Element of the carrier of (X)
the Mult of (X) . (RBLOP,seq) is set
RBLOP * seq1 is Element of the carrier of (X)
the Mult of (X) . (RBLOP,seq1) is set
(RBLOP * seq) + (RBLOP * seq1) is Element of the carrier of (X)
the addF of (X) . ((RBLOP * seq),(RBLOP * seq1)) is Element of the carrier of (X)
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g1 + g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g1,g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
RBLOP * (g1 + g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (RBLOP,(g1 + g)) is set
RBLOP * g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (RBLOP,g1) is set
RBLOP * g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (RBLOP,g) is set
(RBLOP * g1) + (RBLOP * g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((RBLOP * g1),(RBLOP * g)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the carrier of (X) is non empty set
RBLOP is V11() real ext-real set
seq is V11() real ext-real set
RBLOP + seq is V11() real ext-real set
seq1 is Element of the carrier of (X)
(RBLOP + seq) * seq1 is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . ((RBLOP + seq),seq1) is set
RBLOP * seq1 is Element of the carrier of (X)
the Mult of (X) . (RBLOP,seq1) is set
seq * seq1 is Element of the carrier of (X)
the Mult of (X) . (seq,seq1) is set
(RBLOP * seq1) + (seq * seq1) is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . ((RBLOP * seq1),(seq * seq1)) is Element of the carrier of (X)
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(RBLOP + seq) * g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((RBLOP + seq),g1) is set
RBLOP * g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (RBLOP,g1) is set
seq * g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (seq,g1) is set
(RBLOP * g1) + (seq * g1) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((RBLOP * g1),(seq * g1)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the carrier of (X) is non empty set
RBLOP is V11() real ext-real set
seq is V11() real ext-real set
RBLOP * seq is V11() real ext-real set
seq1 is Element of the carrier of (X)
(RBLOP * seq) * seq1 is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . ((RBLOP * seq),seq1) is set
seq * seq1 is Element of the carrier of (X)
the Mult of (X) . (seq,seq1) is set
RBLOP * (seq * seq1) is Element of the carrier of (X)
the Mult of (X) . (RBLOP,(seq * seq1)) is set
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(RBLOP * seq) * g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((RBLOP * seq),g1) is set
seq * g1 is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (seq,g1) is set
RBLOP * (seq * g1) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (RBLOP,(seq * g1)) is set
the carrier of (X) is non empty set
RBLOP is Element of the carrier of (X)
seq is Element of the carrier of (X)
RBLOP * seq is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (RBLOP,seq) is Element of the carrier of (X)
seq1 is V11() real ext-real Element of REAL
seq1 * (RBLOP * seq) is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . (seq1,(RBLOP * seq)) is set
seq1 * RBLOP is Element of the carrier of (X)
the Mult of (X) . (seq1,RBLOP) is set
(seq1 * RBLOP) * seq is Element of the carrier of (X)
the multF of (X) . ((seq1 * RBLOP),seq) is Element of the carrier of (X)
g is Element of BoundedLinearOperators (X,X)
g1 is Element of BoundedLinearOperators (X,X)
(X,g,g1) is Element of BoundedLinearOperators (X,X)
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (g1,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,g,g1),seq1) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (seq1,(X,g,g1)) is Element of BoundedLinearOperators (X,X)
(X,g1,seq1) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (seq1,g1) is Element of BoundedLinearOperators (X,X)
(X,g,(X,g1,seq1)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,g1,seq1),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans ((X,g1,seq1),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative V134() strict vector-associative unital associative right-distributive right_unital AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
X is V15() Function-like V25( NAT ) V29( NAT , the carrier of l1_Space) Element of bool [:NAT, the carrier of l1_Space:]
2 is non empty natural V11() real V13() V32() ext-real positive non negative V51() V52() V53() V54() V55() V56() Element of NAT
1 / 2 is V11() real ext-real non negative Element of COMPLEX
(1 / 2) GeoSeq is V15() Function-like V25( NAT ) V29( NAT , REAL ) V36() V37() V38() Element of bool [:NAT,REAL:]
abs (1 / 2) is V11() real ext-real Element of REAL
c₂ is V15() Function-like V25( NAT ) V29( NAT , REAL ) V36() V37() V38() Element of bool [:NAT,REAL:]
UNIT is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
c₂ . UNIT is V11() real ext-real Element of REAL
UNIT + 1 is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
c₂ . (UNIT + 1) is V11() real ext-real Element of REAL
(c₂ . UNIT) * (1 / 2) is V11() real ext-real Element of REAL
c₂ . 0 is V11() real ext-real Element of REAL
seq_id c₂ is V15() Function-like V25( NAT ) V29( NAT , REAL ) V36() V37() V38() Element of bool [:NAT,REAL:]
UNIT is left_complementable right_complementable complementable Element of the carrier of l1_Space
seq_id UNIT is V15() Function-like V25( NAT ) V29( NAT , REAL ) V36() V37() V38() Element of bool [:NAT,REAL:]
(seq_id UNIT) . 0 is V11() real ext-real Element of REAL
X is non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the carrier of X is non empty non trivial set
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
c₂ is left_complementable right_complementable complementable Element of the carrier of X
||.c₂.|| is V11() real ext-real Element of REAL
the normF of X is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, REAL ) V36() V37() V38() Element of bool [: the carrier of X,REAL:]
[: the carrier of X,REAL:] is V15() V36() V37() V38() set
bool [: the carrier of X,REAL:] is set
the normF of X . c₂ is V11() real ext-real Element of REAL
||.c₂.|| " is V11() real ext-real Element of REAL
(||.c₂.|| ") * c₂ is left_complementable right_complementable complementable Element of the carrier of X
the Mult of X is V15() Function-like V25([:REAL, the carrier of X:]) V29([:REAL, the carrier of X:], the carrier of X) Element of bool [:[:REAL, the carrier of X:], the carrier of X:]
[:REAL, the carrier of X:] is V15() set
[:[:REAL, the carrier of X:], the carrier of X:] is V15() set
bool [:[:REAL, the carrier of X:], the carrier of X:] is set
the Mult of X . ((||.c₂.|| "),c₂) is set
MULT is left_complementable right_complementable complementable Element of the carrier of X
||.MULT.|| is V11() real ext-real Element of REAL
the normF of X . MULT is V11() real ext-real Element of REAL
abs (||.c₂.|| ") is V11() real ext-real Element of REAL
1 * (||.c₂.|| ") is V11() real ext-real Element of REAL
abs (1 * (||.c₂.|| ")) is V11() real ext-real Element of REAL
1 / ||.c₂.|| is V11() real ext-real Element of COMPLEX
abs (1 / ||.c₂.||) is V11() real ext-real Element of REAL
abs ||.c₂.|| is V11() real ext-real Element of REAL
1 / (abs ||.c₂.||) is V11() real ext-real Element of COMPLEX
(abs ||.c₂.||) " is V11() real ext-real Element of REAL
1 * ((abs ||.c₂.||) ") is V11() real ext-real Element of REAL
(abs (||.c₂.|| ")) * ||.c₂.|| is V11() real ext-real Element of REAL
X is non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty non trivial set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
(BoundedLinearOperatorsNorm (X,X)) . (id the carrier of X) is V11() real ext-real Element of REAL
c₂ is left_complementable right_complementable complementable Element of the carrier of X
||.c₂.|| is V11() real ext-real Element of REAL
the normF of X is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, REAL ) V36() V37() V38() Element of bool [: the carrier of X,REAL:]
[: the carrier of X,REAL:] is V15() V36() V37() V38() set
bool [: the carrier of X,REAL:] is set
the normF of X . c₂ is V11() real ext-real Element of REAL
MULT is V11() real ext-real Element of REAL
UNIT is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
PreNorms UNIT is non empty V51() V52() V53() Element of bool REAL
{ ||.(UNIT . b₁).|| where b₁ is left_complementable right_complementable complementable Element of the carrier of X : ||.b₁.|| <= 1 } is set
ADD is left_complementable right_complementable complementable Element of the carrier of X
UNIT . ADD is left_complementable right_complementable complementable Element of the carrier of X
||.(UNIT . ADD).|| is V11() real ext-real Element of REAL
the normF of X . (UNIT . ADD) is V11() real ext-real Element of REAL
||.ADD.|| is V11() real ext-real Element of REAL
the normF of X . ADD is V11() real ext-real Element of REAL
UNIT . c₂ is left_complementable right_complementable complementable Element of the carrier of X
upper_bound (PreNorms UNIT) is V11() real ext-real Element of REAL
MULT is V11() real ext-real set
the non empty set is non empty set
[: the non empty set , the non empty set :] is V15() set
[:[: the non empty set , the non empty set :], the non empty set :] is V15() set
bool [:[: the non empty set , the non empty set :], the non empty set :] is set
the V15() Function-like V25([: the non empty set , the non empty set :]) V29([: 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 V15() Function-like V25([: the non empty set , the non empty set :]) V29([: 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 :]
[:REAL, the non empty set :] is V15() set
[:[:REAL, the non empty set :], the non empty set :] is V15() set
bool [:[:REAL, the non empty set :], the non empty set :] is set
the V15() Function-like V25([:REAL, the non empty set :]) V29([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, the non empty set :], the non empty set :] is V15() Function-like V25([:REAL, the non empty set :]) V29([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, 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 V15() V36() V37() V38() set
bool [: the non empty set ,REAL:] is set
the non empty V15() Function-like V25( the non empty set ) V29( the non empty set , REAL ) V36() V37() V38() Element of bool [: the non empty set ,REAL:] is non empty V15() Function-like V25( the non empty set ) V29( the non empty set , REAL ) V36() V37() V38() Element of bool [: the non empty set ,REAL:]
( the non empty set , the V15() Function-like V25([: the non empty set , the non empty set :]) V29([: 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 V15() Function-like V25([: the non empty set , the non empty set :]) V29([: 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 V15() Function-like V25([:REAL, the non empty set :]) V29([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, 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 V15() Function-like V25( the non empty set ) V29( the non empty set , REAL ) V36() V37() V38() Element of bool [: the non empty set ,REAL:]) is () ()
the carrier of ( the non empty set , the V15() Function-like V25([: the non empty set , the non empty set :]) V29([: 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 V15() Function-like V25([: the non empty set , the non empty set :]) V29([: 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 V15() Function-like V25([:REAL, the non empty set :]) V29([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, 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 V15() Function-like V25( the non empty set ) V29( the non empty set , REAL ) V36() V37() V38() Element of bool [: the non empty set ,REAL:]) is set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
the carrier of (X) is non empty set
UNIT is Element of the carrier of (X)
MULT is Element of the carrier of (X)
UNIT * MULT is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (UNIT,MULT) is Element of the carrier of (X)
ADD is Element of BoundedLinearOperators (X,X)
(X,(X),ADD) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (ADD,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (ADD,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
MULT * UNIT is Element of the carrier of (X)
the multF of (X) . (MULT,UNIT) is Element of the carrier of (X)
(X,ADD,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (ADD,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
the carrier of (X) is non empty set
c₂ is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
UNIT * c₂ is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT is Element of the carrier of (X)
c₂ * MULT is Element of the carrier of (X)
the multF of (X) . (c₂,MULT) is Element of the carrier of (X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty unital () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
the carrier of (X) is non empty set
0. (X) is V80((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
1. (X) is Element of the carrier of (X)
the OneF of (X) is Element of the carrier of (X)
c₂ is Element of the carrier of (X)
UNIT is Element of the carrier of (X)
c₂ + UNIT is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (c₂,UNIT) is Element of the carrier of (X)
UNIT + c₂ is Element of the carrier of (X)
the addF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT is Element of the carrier of (X)
(c₂ + UNIT) + MULT is Element of the carrier of (X)
the addF of (X) . ((c₂ + UNIT),MULT) is Element of the carrier of (X)
UNIT + MULT is Element of the carrier of (X)
the addF of (X) . (UNIT,MULT) is Element of the carrier of (X)
c₂ + (UNIT + MULT) is Element of the carrier of (X)
the addF of (X) . (c₂,(UNIT + MULT)) is Element of the carrier of (X)
c₂ + (0. (X)) is Element of the carrier of (X)
the addF of (X) . (c₂,(0. (X))) is Element of the carrier of (X)
c₂ * UNIT is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . (c₂,UNIT) is Element of the carrier of (X)
(c₂ * UNIT) * MULT is Element of the carrier of (X)
the multF of (X) . ((c₂ * UNIT),MULT) is Element of the carrier of (X)
UNIT * MULT is Element of the carrier of (X)
the multF of (X) . (UNIT,MULT) is Element of the carrier of (X)
c₂ * (UNIT * MULT) is Element of the carrier of (X)
the multF of (X) . (c₂,(UNIT * MULT)) is Element of the carrier of (X)
c₂ * (1. (X)) is Element of the carrier of (X)
the multF of (X) . (c₂,(1. (X))) is Element of the carrier of (X)
(1. (X)) * c₂ is Element of the carrier of (X)
the multF of (X) . ((1. (X)),c₂) is Element of the carrier of (X)
c₂ * (UNIT + MULT) is Element of the carrier of (X)
the multF of (X) . (c₂,(UNIT + MULT)) is Element of the carrier of (X)
c₂ * MULT is Element of the carrier of (X)
the multF of (X) . (c₂,MULT) is Element of the carrier of (X)
(c₂ * UNIT) + (c₂ * MULT) is Element of the carrier of (X)
the addF of (X) . ((c₂ * UNIT),(c₂ * MULT)) is Element of the carrier of (X)
(UNIT + MULT) * c₂ is Element of the carrier of (X)
the multF of (X) . ((UNIT + MULT),c₂) is Element of the carrier of (X)
UNIT * c₂ is Element of the carrier of (X)
the multF of (X) . (UNIT,c₂) is Element of the carrier of (X)
MULT * c₂ is Element of the carrier of (X)
the multF of (X) . (MULT,c₂) is Element of the carrier of (X)
(UNIT * c₂) + (MULT * c₂) is Element of the carrier of (X)
the addF of (X) . ((UNIT * c₂),(MULT * c₂)) is Element of the carrier of (X)
1 * c₂ is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . (1,c₂) is set
ADD is V11() real ext-real set
ADD * (c₂ * UNIT) is Element of the carrier of (X)
the Mult of (X) . (ADD,(c₂ * UNIT)) is set
ADD * c₂ is Element of the carrier of (X)
the Mult of (X) . (ADD,c₂) is set
(ADD * c₂) * UNIT is Element of the carrier of (X)
the multF of (X) . ((ADD * c₂),UNIT) is Element of the carrier of (X)
BS is V11() real ext-real set
ADD * BS is V11() real ext-real set
(ADD * BS) * (c₂ * UNIT) is Element of the carrier of (X)
the Mult of (X) . ((ADD * BS),(c₂ * UNIT)) is set
BS * UNIT is Element of the carrier of (X)
the Mult of (X) . (BS,UNIT) is set
(ADD * c₂) * (BS * UNIT) is Element of the carrier of (X)
the multF of (X) . ((ADD * c₂),(BS * UNIT)) is Element of the carrier of (X)
ADD * (c₂ + UNIT) is Element of the carrier of (X)
the Mult of (X) . (ADD,(c₂ + UNIT)) is set
ADD * UNIT is Element of the carrier of (X)
the Mult of (X) . (ADD,UNIT) is set
(ADD * c₂) + (ADD * UNIT) is Element of the carrier of (X)
the addF of (X) . ((ADD * c₂),(ADD * UNIT)) is Element of the carrier of (X)
ADD + BS is V11() real ext-real set
(ADD + BS) * c₂ is Element of the carrier of (X)
the Mult of (X) . ((ADD + BS),c₂) is set
BS * c₂ is Element of the carrier of (X)
the Mult of (X) . (BS,c₂) is set
(ADD * c₂) + (BS * c₂) is Element of the carrier of (X)
the addF of (X) . ((ADD * c₂),(BS * c₂)) is Element of the carrier of (X)
(ADD * BS) * c₂ is Element of the carrier of (X)
the Mult of (X) . ((ADD * BS),c₂) is set
ADD * (BS * c₂) is Element of the carrier of (X)
the Mult of (X) . (ADD,(BS * c₂)) is set
RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty set
n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
n + g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[: the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #), the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (n,g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
h is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(n + g) + h is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((n + g),h) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
g + h is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (g,h) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
n + (g + h) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (n,(g + h)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V80( RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the ZeroF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
n + (0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (n,(0. RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #))) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
xx is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
n + xx is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (n,xx) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
yy is Element of the carrier of (X)
c₂ + yy is Element of the carrier of (X)
the addF of (X) . (c₂,yy) is Element of the carrier of (X)
yy is Element of BoundedLinearOperators (X,X)
xx is Element of BoundedLinearOperators (X,X)
(X,yy,xx) is Element of BoundedLinearOperators (X,X)
modetrans (yy,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans (xx,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (yy,X,X)),(modetrans (xx,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
zz is Element of BoundedLinearOperators (X,X)
(X) . ((X,yy,xx),zz) is Element of BoundedLinearOperators (X,X)
(X,zz,(X,yy,xx)) is Element of BoundedLinearOperators (X,X)
modetrans (zz,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,yy,xx),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (zz,X,X)),(modetrans ((X,yy,xx),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,zz,yy) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (zz,X,X)),(modetrans (yy,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,zz,yy),xx) is Element of BoundedLinearOperators (X,X)
modetrans ((X,zz,yy),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,zz,yy),X,X)),(modetrans (xx,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X) . (xx,(X,zz,yy)) is Element of BoundedLinearOperators (X,X)
(X,(X),xx) is Element of BoundedLinearOperators (X,X)
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X),X,X)),(modetrans (xx,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,xx,(X)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (xx,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,yy,zz) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (yy,zz) is Element of BoundedLinearOperators (X,X)
(X,(X,yy,zz),xx) is Element of BoundedLinearOperators (X,X)
modetrans ((X,yy,zz),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,yy,zz),X,X)),(modetrans (xx,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,zz,xx) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (zz,X,X)),(modetrans (xx,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,yy,xx),(X,zz,xx)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,yy,xx),(X,zz,xx)) is Element of BoundedLinearOperators (X,X)
(X) . (xx,zz) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,yy,xx),((X) . (xx,zz))) is Element of BoundedLinearOperators (X,X)
(X,xx,(X,yy,zz)) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (xx,X,X)),(modetrans ((X,yy,zz),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,xx,yy) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (xx,X,X)),(modetrans (yy,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,xx,zz) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (xx,X,X)),(modetrans (zz,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,xx,yy),(X,xx,zz)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,xx,yy),(X,xx,zz)) is Element of BoundedLinearOperators (X,X)
(X) . (zz,xx) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,xx,yy),((X) . (zz,xx))) is Element of BoundedLinearOperators (X,X)
BLOP is V11() real ext-real Element of REAL
(X,(X,yy,xx),BLOP) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (BLOP,(X,yy,xx)) is Element of BoundedLinearOperators (X,X)
(X,xx,BLOP) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (BLOP,xx) is Element of BoundedLinearOperators (X,X)
(X,yy,(X,xx,BLOP)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,xx,BLOP),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (yy,X,X)),(modetrans ((X,xx,BLOP),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
RBLOP is V11() real ext-real Element of REAL
BLOP * RBLOP is V11() real ext-real Element of REAL
(X,(X,yy,xx),(BLOP * RBLOP)) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((BLOP * RBLOP),(X,yy,xx)) is Element of BoundedLinearOperators (X,X)
(X,yy,RBLOP) is Element of BoundedLinearOperators (X,X)
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (RBLOP,yy) is Element of BoundedLinearOperators (X,X)
(X,(X,yy,RBLOP),(X,xx,BLOP)) is Element of BoundedLinearOperators (X,X)
modetrans ((X,yy,RBLOP),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans ((X,yy,RBLOP),X,X)),(modetrans ((X,xx,BLOP),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
ADD * (n + g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is V15() Function-like V25([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]) V29([:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)) Element of bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):]
[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
[:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is V15() set
bool [:[:REAL, the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):], the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #):] is set
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,(n + g)) is set
ADD * n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,n) is set
ADD * g is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,g) is set
(ADD * n) + (ADD * g) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD * n),(ADD * g)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(ADD + BS) * n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD + BS),n) is set
BS * n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (BS,n) is set
(ADD * n) + (BS * n) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the addF of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD * n),(BS * n)) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
(ADD * BS) * n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . ((ADD * BS),n) is set
ADD * (BS * n) is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (ADD,(BS * n)) is set
1 * n is left_complementable right_complementable complementable Element of the carrier of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #)
the Mult of RLSStruct(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) . (1,n) is set
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty unital () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
R_NormSpace_of_BoundedLinearOperators (X,X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
NORMSTR(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X)) #) is non empty strict NORMSTR
0. (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V80( R_NormSpace_of_BoundedLinearOperators (X,X)) left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty set
the ZeroF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
||.(0. (R_NormSpace_of_BoundedLinearOperators (X,X))).|| is empty V11() real V15() non-empty empty-yielding V19( RAT ) Function-like one-to-one constant functional ext-real non positive non negative V36() V37() V38() V39() V51() V52() V53() V54() V55() V56() V57() Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty V15() Function-like V25( the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) V29( the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), REAL ) V36() V37() V38() Element of bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)),REAL:]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)),REAL:] is set
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (0. (R_NormSpace_of_BoundedLinearOperators (X,X))) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . (0. (R_NormSpace_of_BoundedLinearOperators (X,X))) is V11() real ext-real Element of REAL
0. (X) is V80((X)) Element of the carrier of (X)
the carrier of (X) is non empty set
the ZeroF of (X) is Element of the carrier of (X)
||.(0. (X)).|| is V11() real ext-real Element of REAL
the normF of (X) is non empty V15() Function-like V25( the carrier of (X)) V29( the carrier of (X), REAL ) V36() V37() V38() Element of bool [: the carrier of (X),REAL:]
[: the carrier of (X),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (X),REAL:] is set
the normF of (X) . (0. (X)) is V11() real ext-real Element of REAL
BLOP is Element of the carrier of (X)
RBLOP is Element of the carrier of (X)
seq1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
||.seq1.|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . seq1 is V11() real ext-real Element of REAL
g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
||.g1.|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . g1 is V11() real ext-real Element of REAL
||.seq1.|| + ||.g1.|| is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . seq1 is V11() real ext-real Element of REAL
((BoundedLinearOperatorsNorm (X,X)) . seq1) + ||.g1.|| is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . g1 is V11() real ext-real Element of REAL
((BoundedLinearOperatorsNorm (X,X)) . seq1) + ((BoundedLinearOperatorsNorm (X,X)) . g1) is V11() real ext-real Element of REAL
||.BLOP.|| is V11() real ext-real Element of REAL
the normF of (X) . BLOP is V11() real ext-real Element of REAL
the normF of (X) . RBLOP is V11() real ext-real Element of REAL
||.BLOP.|| + ( the normF of (X) . RBLOP) is V11() real ext-real Element of REAL
||.RBLOP.|| is V11() real ext-real Element of REAL
the normF of (X) . RBLOP is V11() real ext-real Element of REAL
||.BLOP.|| + ||.RBLOP.|| is V11() real ext-real Element of REAL
BLOP + RBLOP is Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (BLOP,RBLOP) is Element of the carrier of (X)
||.(BLOP + RBLOP).|| is V11() real ext-real Element of REAL
the normF of (X) . (BLOP + RBLOP) is V11() real ext-real Element of REAL
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (BLOP,RBLOP) is set
(BoundedLinearOperatorsNorm (X,X)) . ((Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (BLOP,RBLOP)) is V11() real ext-real Element of REAL
seq1 + g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (seq1,g1) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
||.(seq1 + g1).|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (seq1 + g1) is V11() real ext-real Element of REAL
seq is V11() real ext-real Element of REAL
seq * BLOP is Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . (seq,BLOP) is set
||.(seq * BLOP).|| is V11() real ext-real Element of REAL
the normF of (X) . (seq * BLOP) is V11() real ext-real Element of REAL
(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (seq,BLOP) is set
(BoundedLinearOperatorsNorm (X,X)) . ((Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (seq,BLOP)) is V11() real ext-real Element of REAL
seq * seq1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (seq,seq1) is set
||.(seq * seq1).|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . (seq * seq1) is V11() real ext-real Element of REAL
abs seq is V11() real ext-real Element of REAL
(abs seq) * ||.BLOP.|| is V11() real ext-real Element of REAL
BLOP is Element of the carrier of (X)
seq is Element of the carrier of (X)
BLOP is V11() real ext-real set
RBLOP is V11() real ext-real set
BLOP + RBLOP is V11() real ext-real set
(BLOP + RBLOP) * seq is Element of the carrier of (X)
the Mult of (X) . ((BLOP + RBLOP),seq) is set
BLOP * seq is Element of the carrier of (X)
the Mult of (X) . (BLOP,seq) is set
RBLOP * seq is Element of the carrier of (X)
the Mult of (X) . (RBLOP,seq) is set
(BLOP * seq) + (RBLOP * seq) is Element of the carrier of (X)
the addF of (X) . ((BLOP * seq),(RBLOP * seq)) is Element of the carrier of (X)
g is Element of the carrier of (X)
seq1 is V11() real ext-real set
g1 is V11() real ext-real set
seq1 * g1 is V11() real ext-real set
(seq1 * g1) * g is Element of the carrier of (X)
the Mult of (X) . ((seq1 * g1),g) is set
g1 * g is Element of the carrier of (X)
the Mult of (X) . (g1,g) is set
seq1 * (g1 * g) is Element of the carrier of (X)
the Mult of (X) . (seq1,(g1 * g)) is set
1. (X) is Element of the carrier of (X)
the OneF of (X) is Element of the carrier of (X)
BLOP is Element of the carrier of (X)
RBLOP is Element of the carrier of (X)
BLOP + RBLOP is Element of the carrier of (X)
the addF of (X) . (BLOP,RBLOP) is Element of the carrier of (X)
RBLOP + BLOP is Element of the carrier of (X)
the addF of (X) . (RBLOP,BLOP) is Element of the carrier of (X)
seq is Element of the carrier of (X)
seq1 is Element of the carrier of (X)
seq + seq1 is Element of the carrier of (X)
the addF of (X) . (seq,seq1) is Element of the carrier of (X)
g1 is Element of the carrier of (X)
(seq + seq1) + g1 is Element of the carrier of (X)
the addF of (X) . ((seq + seq1),g1) is Element of the carrier of (X)
seq1 + g1 is Element of the carrier of (X)
the addF of (X) . (seq1,g1) is Element of the carrier of (X)
seq + (seq1 + g1) is Element of the carrier of (X)
the addF of (X) . (seq,(seq1 + g1)) is Element of the carrier of (X)
g is Element of the carrier of (X)
g + (0. (X)) is Element of the carrier of (X)
the addF of (X) . (g,(0. (X))) is Element of the carrier of (X)
r is Element of the carrier of (X)
m is Element of the carrier of (X)
n is Element of the carrier of (X)
m * n is Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . (m,n) is Element of the carrier of (X)
g is Element of the carrier of (X)
(m * n) * g is Element of the carrier of (X)
the multF of (X) . ((m * n),g) is Element of the carrier of (X)
n * g is Element of the carrier of (X)
the multF of (X) . (n,g) is Element of the carrier of (X)
m * (n * g) is Element of the carrier of (X)
the multF of (X) . (m,(n * g)) is Element of the carrier of (X)
h is Element of the carrier of (X)
h * (1. (X)) is Element of the carrier of (X)
the multF of (X) . (h,(1. (X))) is Element of the carrier of (X)
xx is Element of the carrier of (X)
(1. (X)) * xx is Element of the carrier of (X)
the multF of (X) . ((1. (X)),xx) is Element of the carrier of (X)
yy is Element of the carrier of (X)
zz is Element of the carrier of (X)
c₂₁ is Element of the carrier of (X)
zz + c₂₁ is Element of the carrier of (X)
the addF of (X) . (zz,c₂₁) is Element of the carrier of (X)
yy * (zz + c₂₁) is Element of the carrier of (X)
the multF of (X) . (yy,(zz + c₂₁)) is Element of the carrier of (X)
yy * zz is Element of the carrier of (X)
the multF of (X) . (yy,zz) is Element of the carrier of (X)
yy * c₂₁ is Element of the carrier of (X)
the multF of (X) . (yy,c₂₁) is Element of the carrier of (X)
(yy * zz) + (yy * c₂₁) is Element of the carrier of (X)
the addF of (X) . ((yy * zz),(yy * c₂₁)) is Element of the carrier of (X)
c₂₃ is Element of the carrier of (X)
c₂₄ is Element of the carrier of (X)
c₂₃ + c₂₄ is Element of the carrier of (X)
the addF of (X) . (c₂₃,c₂₄) is Element of the carrier of (X)
c₂₂ is Element of the carrier of (X)
(c₂₃ + c₂₄) * c₂₂ is Element of the carrier of (X)
the multF of (X) . ((c₂₃ + c₂₄),c₂₂) is Element of the carrier of (X)
c₂₃ * c₂₂ is Element of the carrier of (X)
the multF of (X) . (c₂₃,c₂₂) is Element of the carrier of (X)
c₂₄ * c₂₂ is Element of the carrier of (X)
the multF of (X) . (c₂₄,c₂₂) is Element of the carrier of (X)
(c₂₃ * c₂₂) + (c₂₄ * c₂₂) is Element of the carrier of (X)
the addF of (X) . ((c₂₃ * c₂₂),(c₂₄ * c₂₂)) is Element of the carrier of (X)
c₂₅ is Element of the carrier of (X)
c₂₆ is Element of the carrier of (X)
c₂₅ * c₂₆ is Element of the carrier of (X)
the multF of (X) . (c₂₅,c₂₆) is Element of the carrier of (X)
c₂₇ is V11() real ext-real Element of REAL
c₂₇ * (c₂₅ * c₂₆) is Element of the carrier of (X)
the Mult of (X) . (c₂₇,(c₂₅ * c₂₆)) is set
c₂₇ * c₂₅ is Element of the carrier of (X)
the Mult of (X) . (c₂₇,c₂₅) is set
(c₂₇ * c₂₅) * c₂₆ is Element of the carrier of (X)
the multF of (X) . ((c₂₇ * c₂₅),c₂₆) is Element of the carrier of (X)
c₂₈ is Element of the carrier of (X)
c₂₉ is Element of the carrier of (X)
c₂₈ * c₂₉ is Element of the carrier of (X)
the multF of (X) . (c₂₈,c₂₉) is Element of the carrier of (X)
c₃₀ is V11() real ext-real Element of REAL
c₃₁ is V11() real ext-real Element of REAL
c₃₀ * c₃₁ is V11() real ext-real Element of REAL
(c₃₀ * c₃₁) * (c₂₈ * c₂₉) is Element of the carrier of (X)
the Mult of (X) . ((c₃₀ * c₃₁),(c₂₈ * c₂₉)) is set
c₃₀ * c₂₈ is Element of the carrier of (X)
the Mult of (X) . (c₃₀,c₂₈) is set
c₃₁ * c₂₉ is Element of the carrier of (X)
the Mult of (X) . (c₃₁,c₂₉) is set
(c₃₀ * c₂₈) * (c₃₁ * c₂₉) is Element of the carrier of (X)
the multF of (X) . ((c₃₀ * c₂₈),(c₃₁ * c₂₉)) is Element of the carrier of (X)
c₃₂ is Element of the carrier of (X)
c₃₃ is Element of the carrier of (X)
c₃₂ + c₃₃ is Element of the carrier of (X)
the addF of (X) . (c₃₂,c₃₃) is Element of the carrier of (X)
c₃₄ is V11() real ext-real Element of REAL
c₃₄ * (c₃₂ + c₃₃) is Element of the carrier of (X)
the Mult of (X) . (c₃₄,(c₃₂ + c₃₃)) is set
c₃₄ * c₃₂ is Element of the carrier of (X)
the Mult of (X) . (c₃₄,c₃₂) is set
c₃₄ * c₃₃ is Element of the carrier of (X)
the Mult of (X) . (c₃₄,c₃₃) is set
(c₃₄ * c₃₂) + (c₃₄ * c₃₃) is Element of the carrier of (X)
the addF of (X) . ((c₃₄ * c₃₂),(c₃₄ * c₃₃)) is Element of the carrier of (X)
c₃₅ is Element of the carrier of (X)
c₃₆ is V11() real ext-real Element of REAL
c₃₇ is V11() real ext-real Element of REAL
c₃₆ + c₃₇ is V11() real ext-real Element of REAL
(c₃₆ + c₃₇) * c₃₅ is Element of the carrier of (X)
the Mult of (X) . ((c₃₆ + c₃₇),c₃₅) is set
c₃₆ * c₃₅ is Element of the carrier of (X)
the Mult of (X) . (c₃₆,c₃₅) is set
c₃₇ * c₃₅ is Element of the carrier of (X)
the Mult of (X) . (c₃₇,c₃₅) is set
(c₃₆ * c₃₅) + (c₃₇ * c₃₅) is Element of the carrier of (X)
the addF of (X) . ((c₃₆ * c₃₅),(c₃₇ * c₃₅)) is Element of the carrier of (X)
c₃₈ is Element of the carrier of (X)
c₃₉ is V11() real ext-real Element of REAL
c₄₀ is V11() real ext-real Element of REAL
c₃₉ * c₄₀ is V11() real ext-real Element of REAL
(c₃₉ * c₄₀) * c₃₈ is Element of the carrier of (X)
the Mult of (X) . ((c₃₉ * c₄₀),c₃₈) is set
c₄₀ * c₃₈ is Element of the carrier of (X)
the Mult of (X) . (c₄₀,c₃₈) is set
c₃₉ * (c₄₀ * c₃₈) is Element of the carrier of (X)
the Mult of (X) . (c₃₉,(c₄₀ * c₃₈)) is set
c₄₁ is Element of the carrier of (X)
1 * c₄₁ is Element of the carrier of (X)
the Mult of (X) . (1,c₄₁) is set
c₄₃ is Element of the carrier of (X)
c₄₄ is Element of the carrier of (X)
c₄₃ + c₄₄ is Element of the carrier of (X)
the addF of (X) . (c₄₃,c₄₄) is Element of the carrier of (X)
c₄₂ is V11() real ext-real set
c₄₂ * (c₄₃ + c₄₄) is Element of the carrier of (X)
the Mult of (X) . (c₄₂,(c₄₃ + c₄₄)) is set
c₄₂ * c₄₃ is Element of the carrier of (X)
the Mult of (X) . (c₄₂,c₄₃) is set
c₄₂ * c₄₄ is Element of the carrier of (X)
the Mult of (X) . (c₄₂,c₄₄) is set
(c₄₂ * c₄₃) + (c₄₂ * c₄₄) is Element of the carrier of (X)
the addF of (X) . ((c₄₂ * c₄₃),(c₄₂ * c₄₄)) is Element of the carrier of (X)
the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty unital () ()
BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))
R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))
the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR is non empty set
RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty functional M4( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )
FuncZero ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is V15() Function-like V25( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) V29( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) Element of K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )
0. the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR is V80( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) left_complementable right_complementable complementable Element of the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
the ZeroF of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR is left_complementable right_complementable complementable Element of the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
K308( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ,(0. the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) is non empty V15() Function-like V25( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) V29( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) Element of bool [: the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR :]
[: the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR :] is V15() set
bool [: the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR :] is set
FuncAdd ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is V15() Function-like V25([:K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):]) V29([:K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):]
[:K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):] is V15() set
[:[:K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):] is V15() set
bool [:[:K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):] is set
FuncExtMult ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is V15() Function-like V25([:REAL,K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):]) V29([:REAL,K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:REAL,K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):]
[:REAL,K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):] is V15() set
[:[:REAL,K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):] is V15() set
bool [:[:REAL,K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):],K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ):] is set
RLSStruct(# K138( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),(FuncZero ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(FuncAdd ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(FuncExtMult ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) is non empty set
bool the carrier of (RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) is set
Zero_ ((LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is V15() Function-like Element of LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )
Add_ ((LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is V15() Function-like V25([:(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]) V29([:(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):], LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]
[:(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
[:[:(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
bool [:[:(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is set
Mult_ ((LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is V15() Function-like V25([:REAL,(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]) V29([:REAL,(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):], LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:REAL,(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]
[:REAL,(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
[:[:REAL,(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
bool [:[:REAL,(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is set
RLSStruct(# (LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(Zero_ ((LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )))),(Add_ ((LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )))),(Mult_ ((LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(RealVectSpace ( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) is set
( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is V15() Function-like V25([:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]) V29([:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):], BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]
[:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
[:[:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
bool [:[:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is set
Add_ ((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is V15() Function-like V25([:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]) V29([:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):], BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]
Mult_ ((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is V15() Function-like V25([:REAL,(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]) V29([:REAL,(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):], BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) Element of bool [:[:REAL,(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):]
[:REAL,(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
[:[:REAL,(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is V15() set
bool [:[:REAL,(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):],(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )):] is set
( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is Element of BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )
id the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR is non empty V15() V18( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) V19( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) Function-like one-to-one V25( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) V29( the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) Element of bool [: the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the carrier of the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR :]
Zero_ ((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is Element of BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )
BoundedLinearOperatorsNorm ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ) is non empty V15() Function-like V25( BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )) V29( BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),REAL:]
[:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),REAL:] is set
((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),(Add_ ((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )))),(Mult_ ((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )))),( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ),(Zero_ ((BoundedLinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR )))),(BoundedLinearOperatorsNorm ( the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR , the non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR ))) is () ()
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty unital () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() vector-associative discerning reflexive RealNormSpace-like associative right-distributive right_unital ()
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() vector-associative discerning reflexive RealNormSpace-like associative right-distributive right_unital ()
X is non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR
(X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() vector-associative discerning reflexive RealNormSpace-like unital associative right-distributive right_unital () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty non trivial set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
R_NormSpace_of_BoundedLinearOperators (X,X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR
NORMSTR(# (BoundedLinearOperators (X,X)),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X)) #) is non empty strict NORMSTR
the carrier of (X) is non empty set
seq is left_complementable right_complementable complementable Element of the carrier of (X)
seq1 is left_complementable right_complementable complementable Element of the carrier of (X)
seq * seq1 is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (seq,seq1) is left_complementable right_complementable complementable Element of the carrier of (X)
||.(seq * seq1).|| is V11() real ext-real Element of REAL
the normF of (X) is non empty V15() Function-like V25( the carrier of (X)) V29( the carrier of (X), REAL ) V36() V37() V38() Element of bool [: the carrier of (X),REAL:]
[: the carrier of (X),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (X),REAL:] is set
the normF of (X) . (seq * seq1) is V11() real ext-real Element of REAL
||.seq.|| is V11() real ext-real Element of REAL
the normF of (X) . seq is V11() real ext-real Element of REAL
||.seq1.|| is V11() real ext-real Element of REAL
the normF of (X) . seq1 is V11() real ext-real Element of REAL
||.seq.|| * ||.seq1.|| is V11() real ext-real Element of REAL
g1 is Element of BoundedLinearOperators (X,X)
modetrans (g1,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(BoundedLinearOperatorsNorm (X,X)) . (modetrans (g1,X,X)) is V11() real ext-real Element of REAL
g is Element of BoundedLinearOperators (X,X)
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(BoundedLinearOperatorsNorm (X,X)) . (modetrans (g,X,X)) is V11() real ext-real Element of REAL
((BoundedLinearOperatorsNorm (X,X)) . (modetrans (g1,X,X))) * ((BoundedLinearOperatorsNorm (X,X)) . (modetrans (g,X,X))) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . g1 is V11() real ext-real Element of REAL
((BoundedLinearOperatorsNorm (X,X)) . g1) * ((BoundedLinearOperatorsNorm (X,X)) . (modetrans (g,X,X))) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . g is V11() real ext-real Element of REAL
((BoundedLinearOperatorsNorm (X,X)) . g1) * ((BoundedLinearOperatorsNorm (X,X)) . g) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . seq1 is V11() real ext-real Element of REAL
||.seq.|| * ((BoundedLinearOperatorsNorm (X,X)) . seq1) is V11() real ext-real Element of REAL
(X) . (seq,seq1) is set
(BoundedLinearOperatorsNorm (X,X)) . ((X) . (seq,seq1)) is V11() real ext-real Element of REAL
(X,g,g1) is Element of BoundedLinearOperators (X,X)
(X,(modetrans (g,X,X)),(modetrans (g1,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(BoundedLinearOperatorsNorm (X,X)) . (X,g,g1) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . (X,(modetrans (g,X,X)),(modetrans (g1,X,X))) is V11() real ext-real Element of REAL
1. (X) is left_complementable right_complementable complementable Element of the carrier of (X)
the carrier of (X) is non empty set
the OneF of (X) is left_complementable right_complementable complementable Element of the carrier of (X)
||.(1. (X)).|| is V11() real ext-real Element of REAL
the normF of (X) is non empty V15() Function-like V25( the carrier of (X)) V29( the carrier of (X), REAL ) V36() V37() V38() Element of bool [: the carrier of (X),REAL:]
[: the carrier of (X),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (X),REAL:] is set
the normF of (X) . (1. (X)) is V11() real ext-real Element of REAL
(BoundedLinearOperatorsNorm (X,X)) . (id the carrier of X) is V11() real ext-real Element of REAL
seq is V11() real ext-real Element of REAL
seq1 is left_complementable right_complementable complementable Element of the carrier of (X)
g1 is left_complementable right_complementable complementable Element of the carrier of (X)
seq1 * g1 is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . (seq1,g1) is left_complementable right_complementable complementable Element of the carrier of (X)
seq * (seq1 * g1) is left_complementable right_complementable complementable Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . (seq,(seq1 * g1)) is set
seq * g1 is left_complementable right_complementable complementable Element of the carrier of (X)
the Mult of (X) . (seq,g1) is set
seq1 * (seq * g1) is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) . (seq1,(seq * g1)) is left_complementable right_complementable complementable Element of the carrier of (X)
1 * seq is V11() real ext-real Element of REAL
(1 * seq) * (seq1 * g1) is left_complementable right_complementable complementable Element of the carrier of (X)
the Mult of (X) . ((1 * seq),(seq1 * g1)) is set
1 * seq1 is left_complementable right_complementable complementable Element of the carrier of (X)
the Mult of (X) . (1,seq1) is set
(1 * seq1) * (seq * g1) is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) . ((1 * seq1),(seq * g1)) is left_complementable right_complementable complementable Element of the carrier of (X)
seq is left_complementable right_complementable complementable Element of the carrier of (X)
(1. (X)) * seq is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the multF of (X) . ((1. (X)),seq) is left_complementable right_complementable complementable Element of the carrier of (X)
seq1 is Element of BoundedLinearOperators (X,X)
(X,seq1,(X)) is Element of BoundedLinearOperators (X,X)
modetrans (seq1,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (seq1,X,X)),(modetrans ((X),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
seq1 is left_complementable right_complementable complementable Element of the carrier of (X)
g1 is left_complementable right_complementable complementable Element of the carrier of (X)
seq1 + g1 is left_complementable right_complementable complementable Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . (seq1,g1) is left_complementable right_complementable complementable Element of the carrier of (X)
seq is left_complementable right_complementable complementable Element of the carrier of (X)
(seq1 + g1) * seq is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
the multF of (X) . ((seq1 + g1),seq) is left_complementable right_complementable complementable Element of the carrier of (X)
seq1 * seq is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) . (seq1,seq) is left_complementable right_complementable complementable Element of the carrier of (X)
g1 * seq is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) . (g1,seq) is left_complementable right_complementable complementable Element of the carrier of (X)
(seq1 * seq) + (g1 * seq) is left_complementable right_complementable complementable Element of the carrier of (X)
the addF of (X) . ((seq1 * seq),(g1 * seq)) is left_complementable right_complementable complementable Element of the carrier of (X)
seq1 + g1 is left_complementable right_complementable complementable Element of the carrier of (X)
(seq1 + g1) * seq is left_complementable right_complementable complementable Element of the carrier of (X)
the multF of (X) . ((seq1 + g1),seq) is left_complementable right_complementable complementable Element of the carrier of (X)
g is Element of BoundedLinearOperators (X,X)
r is Element of BoundedLinearOperators (X,X)
m is Element of BoundedLinearOperators (X,X)
(X,r,m) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . (r,m) is Element of BoundedLinearOperators (X,X)
(X,g,(X,r,m)) is Element of BoundedLinearOperators (X,X)
modetrans (g,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
modetrans ((X,r,m),X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans ((X,r,m),X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,r) is Element of BoundedLinearOperators (X,X)
modetrans (r,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans (r,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,g,m) is Element of BoundedLinearOperators (X,X)
modetrans (m,X,X) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(modetrans (g,X,X)),(modetrans (m,X,X))) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) V29( the carrier of X, the carrier of X) V165(X,X) V166(X,X) Lipschitzian Element of bool [: the carrier of X, the carrier of X:]
(X,(X,g,r),(X,g,m)) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,g,r),(X,g,m)) is Element of BoundedLinearOperators (X,X)
(X) . (m,g) is Element of BoundedLinearOperators (X,X)
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((X,g,r),((X) . (m,g))) is Element of BoundedLinearOperators (X,X)
(seq1 * seq) + (g1 * seq) is left_complementable right_complementable complementable Element of the carrier of (X)
[:NAT, the carrier of (X):] is V15() set
bool [:NAT, the carrier of (X):] is set
seq is V15() Function-like V25( NAT ) V29( NAT , the carrier of (X)) Element of bool [:NAT, the carrier of (X):]
the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty set
[:NAT, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:NAT, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
g1 is V11() real ext-real Element of REAL
g is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
r is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
m is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
seq1 is V15() Function-like V25( NAT ) V29( NAT , the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:NAT, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
seq1 . r is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
seq1 . m is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(seq1 . r) - (seq1 . m) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
- (seq1 . m) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(seq1 . r) + (- (seq1 . m)) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((seq1 . r),(- (seq1 . m))) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
||.((seq1 . r) - (seq1 . m)).|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) is non empty V15() Function-like V25( the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) V29( the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)), REAL ) V36() V37() V38() Element of bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)),REAL:]
[: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [: the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)),REAL:] is set
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((seq1 . r) - (seq1 . m)) is V11() real ext-real Element of REAL
(seq1 . r) + (- (seq1 . m)) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(BoundedLinearOperatorsNorm (X,X)) . ((seq1 . r) + (- (seq1 . m))) is V11() real ext-real Element of REAL
(- 1) * (seq1 . m) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) is V15() Function-like V25([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]) V29([:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))) Element of bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):]
[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL, the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):], the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X)):] is set
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((- 1),(seq1 . m)) is set
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq1 . r),((- 1) * (seq1 . m))) is set
(BoundedLinearOperatorsNorm (X,X)) . ((Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq1 . r),((- 1) * (seq1 . m)))) is V11() real ext-real Element of REAL
seq . r is left_complementable right_complementable complementable Element of the carrier of (X)
seq . m is left_complementable right_complementable complementable Element of the carrier of (X)
(- 1) * (seq . m) is left_complementable right_complementable complementable Element of the carrier of (X)
the Mult of (X) is V15() Function-like V25([:REAL, the carrier of (X):]) V29([:REAL, the carrier of (X):], the carrier of (X)) Element of bool [:[:REAL, the carrier of (X):], the carrier of (X):]
[:REAL, the carrier of (X):] is V15() set
[:[:REAL, the carrier of (X):], the carrier of (X):] is V15() set
bool [:[:REAL, the carrier of (X):], the carrier of (X):] is set
the Mult of (X) . ((- 1),(seq . m)) is set
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq . r),((- 1) * (seq . m))) is set
(BoundedLinearOperatorsNorm (X,X)) . ((Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq . r),((- 1) * (seq . m)))) is V11() real ext-real Element of REAL
- (seq . m) is left_complementable right_complementable complementable Element of the carrier of (X)
(seq . r) + (- (seq . m)) is left_complementable right_complementable complementable Element of the carrier of (X)
the addF of (X) is V15() Function-like V25([: the carrier of (X), the carrier of (X):]) V29([: the carrier of (X), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):]
[: the carrier of (X), the carrier of (X):] is V15() set
[:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is V15() set
bool [:[: the carrier of (X), the carrier of (X):], the carrier of (X):] is set
the addF of (X) . ((seq . r),(- (seq . m))) is left_complementable right_complementable complementable Element of the carrier of (X)
(BoundedLinearOperatorsNorm (X,X)) . ((seq . r) + (- (seq . m))) is V11() real ext-real Element of REAL
(seq . r) - (seq . m) is left_complementable right_complementable complementable Element of the carrier of (X)
(seq . r) + (- (seq . m)) is left_complementable right_complementable complementable Element of the carrier of (X)
||.((seq . r) - (seq . m)).|| is V11() real ext-real Element of REAL
the normF of (X) . ((seq . r) - (seq . m)) is V11() real ext-real Element of REAL
g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
r is V11() real ext-real Element of REAL
m is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
n is natural V11() real V13() V32() ext-real V51() V52() V53() V54() V55() V56() Element of NAT
seq1 . n is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(seq1 . n) - g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
- g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(seq1 . n) + (- g1) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the addF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((seq1 . n),(- g1)) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
||.((seq1 . n) - g1).|| is V11() real ext-real Element of REAL
the normF of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((seq1 . n) - g1) is V11() real ext-real Element of REAL
(seq1 . n) + (- g1) is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
(BoundedLinearOperatorsNorm (X,X)) . ((seq1 . n) + (- g1)) is V11() real ext-real Element of REAL
(- 1) * g1 is V15() Function-like left_complementable right_complementable complementable Element of the carrier of (R_NormSpace_of_BoundedLinearOperators (X,X))
the Mult of (R_NormSpace_of_BoundedLinearOperators (X,X)) . ((- 1),g1) is set
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq1 . n),((- 1) * g1)) is set
(BoundedLinearOperatorsNorm (X,X)) . ((Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq1 . n),((- 1) * g1))) is V11() real ext-real Element of REAL
seq . n is left_complementable right_complementable complementable Element of the carrier of (X)
g is left_complementable right_complementable complementable Element of the carrier of (X)
(- 1) * g is left_complementable right_complementable complementable Element of the carrier of (X)
the Mult of (X) . ((- 1),g) is set
(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq . n),((- 1) * g)) is set
(BoundedLinearOperatorsNorm (X,X)) . ((Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) . ((seq . n),((- 1) * g))) is V11() real ext-real Element of REAL
- g is left_complementable right_complementable complementable Element of the carrier of (X)
(seq . n) + (- g) is left_complementable right_complementable complementable Element of the carrier of (X)
the addF of (X) . ((seq . n),(- g)) is left_complementable right_complementable complementable Element of the carrier of (X)
(BoundedLinearOperatorsNorm (X,X)) . ((seq . n) + (- g)) is V11() real ext-real Element of REAL
(seq . n) - g is left_complementable right_complementable complementable Element of the carrier of (X)
(seq . n) + (- g) is left_complementable right_complementable complementable Element of the carrier of (X)
||.((seq . n) - g).|| is V11() real ext-real Element of REAL
the normF of (X) . ((seq . n) - g) is V11() real ext-real Element of REAL
the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR is non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR
( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() vector-associative discerning reflexive RealNormSpace-like unital associative right-distributive left-distributive right_unital distributive left_unital complete () () () () () ()
BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))
R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))
the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR is non empty non trivial set
RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty functional M4( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )
FuncZero ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is V15() Function-like V25( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) V29( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) Element of K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )
0. the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR is V80( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) left_complementable right_complementable complementable Element of the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR
the ZeroF of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR is left_complementable right_complementable complementable Element of the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR
K308( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ,(0. the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) is non empty V15() Function-like V25( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) V29( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) Element of bool [: the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR :]
[: the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR :] is V15() set
bool [: the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR :] is set
FuncAdd ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is V15() Function-like V25([:K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):]) V29([:K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):]
[:K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):] is V15() set
[:[:K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):] is V15() set
bool [:[:K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):] is set
FuncExtMult ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is V15() Function-like V25([:REAL,K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):]) V29([:REAL,K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:REAL,K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):]
[:REAL,K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):] is V15() set
[:[:REAL,K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):] is V15() set
bool [:[:REAL,K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):],K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ):] is set
RLSStruct(# K138( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),(FuncZero ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(FuncAdd ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(FuncExtMult ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) is non empty set
bool the carrier of (RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) is set
Zero_ ((LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is V15() Function-like Element of LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )
Add_ ((LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is V15() Function-like V25([:(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]) V29([:(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):], LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]
[:(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
[:[:(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
bool [:[:(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is set
Mult_ ((LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is V15() Function-like V25([:REAL,(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]) V29([:REAL,(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):], LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:REAL,(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]
[:REAL,(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
[:[:REAL,(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
bool [:[:REAL,(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is set
RLSStruct(# (LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(Zero_ ((LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )))),(Add_ ((LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )))),(Mult_ ((LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(RealVectSpace ( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) is set
( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is V15() Function-like V25([:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]) V29([:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):], BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]
[:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
[:[:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
bool [:[:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is set
Add_ ((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is V15() Function-like V25([:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]) V29([:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):], BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]
Mult_ ((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is V15() Function-like V25([:REAL,(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]) V29([:REAL,(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):], BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) Element of bool [:[:REAL,(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):]
[:REAL,(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
[:[:REAL,(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is V15() set
bool [:[:REAL,(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):],(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )):] is set
( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is Element of BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )
id the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR is non empty V15() V18( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) V19( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) Function-like one-to-one V25( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) V29( the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) Element of bool [: the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the carrier of the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR :]
Zero_ ((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is Element of BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )
BoundedLinearOperatorsNorm ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ) is non empty V15() Function-like V25( BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )) V29( BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),REAL:]
[:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),REAL:] is set
((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),(Add_ ((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )))),(Mult_ ((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )))),( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ),(Zero_ ((BoundedLinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )),(R_VectorSpace_of_LinearOperators ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR )))),(BoundedLinearOperatorsNorm ( the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR , the non empty non trivial left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like complete NORMSTR ))) is () ()
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed V134() unital associative right-distributive left-distributive right_unital distributive left_unital doubleLoopStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
doubleLoopStr(# (BoundedLinearOperators (X,X)),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is non empty strict doubleLoopStr
1. (X) is left_complementable right_complementable complementable Element of the carrier of (X)
the carrier of (X) is non empty set
the OneF of (X) is left_complementable right_complementable complementable Element of the carrier of (X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative V134() strict vector-associative unital associative right-distributive right_unital AlgebraStr
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
AlgebraStr(# (BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))) #) is strict AlgebraStr
1. (X) is left_complementable right_complementable complementable Element of the carrier of (X)
the carrier of (X) is non empty set
the OneF of (X) is left_complementable right_complementable complementable Element of the carrier of (X)
X is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() discerning reflexive RealNormSpace-like NORMSTR
(X) is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() vector-associative discerning reflexive RealNormSpace-like unital associative right-distributive right_unital () ()
BoundedLinearOperators (X,X) is non empty Element of bool the carrier of (R_VectorSpace_of_LinearOperators (X,X))
R_VectorSpace_of_LinearOperators (X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
LinearOperators (X,X) is non empty functional Element of bool the carrier of (RealVectSpace ( the carrier of X,X))
the carrier of X is non empty set
RealVectSpace ( the carrier of X,X) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
K138( the carrier of X, the carrier of X) is non empty functional M4( the carrier of X, the carrier of X)
FuncZero ( the carrier of X,X) is V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of K138( the carrier of X, the carrier of X)
0. X is V80(X) left_complementable right_complementable complementable Element of the carrier of X
the ZeroF of X is left_complementable right_complementable complementable Element of the carrier of X
K308( the carrier of X, the carrier of X,(0. X)) is non empty V15() Function-like V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
[: the carrier of X, the carrier of X:] is V15() set
bool [: the carrier of X, the carrier of X:] is set
FuncAdd ( the carrier of X,X) is V15() Function-like V25([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):]) V29([:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):] is V15() set
[:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:K138( the carrier of X, the carrier of X),K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
FuncExtMult ( the carrier of X,X) is V15() Function-like V25([:REAL,K138( the carrier of X, the carrier of X):]) V29([:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X)) Element of bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):]
[:REAL,K138( the carrier of X, the carrier of X):] is V15() set
[:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is V15() set
bool [:[:REAL,K138( the carrier of X, the carrier of X):],K138( the carrier of X, the carrier of X):] is set
RLSStruct(# K138( the carrier of X, the carrier of X),(FuncZero ( the carrier of X,X)),(FuncAdd ( the carrier of X,X)),(FuncExtMult ( the carrier of X,X)) #) is non empty strict RLSStruct
the carrier of (RealVectSpace ( the carrier of X,X)) is non empty set
bool the carrier of (RealVectSpace ( the carrier of X,X)) is set
Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like Element of LinearOperators (X,X)
Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:(LinearOperators (X,X)),(LinearOperators (X,X)):]) V29([:(LinearOperators (X,X)),(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:(LinearOperators (X,X)),(LinearOperators (X,X)):] is V15() set
[:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:(LinearOperators (X,X)),(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X))) is V15() Function-like V25([:REAL,(LinearOperators (X,X)):]) V29([:REAL,(LinearOperators (X,X)):], LinearOperators (X,X)) Element of bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):]
[:REAL,(LinearOperators (X,X)):] is V15() set
[:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is V15() set
bool [:[:REAL,(LinearOperators (X,X)):],(LinearOperators (X,X)):] is set
RLSStruct(# (LinearOperators (X,X)),(Zero_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Add_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))),(Mult_ ((LinearOperators (X,X)),(RealVectSpace ( the carrier of X,X)))) #) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V134() RLSStruct
the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is non empty set
bool the carrier of (R_VectorSpace_of_LinearOperators (X,X)) is set
(X) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):] is V15() set
[:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):]) V29([:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:(BoundedLinearOperators (X,X)),(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is V15() Function-like V25([:REAL,(BoundedLinearOperators (X,X)):]) V29([:REAL,(BoundedLinearOperators (X,X)):], BoundedLinearOperators (X,X)) Element of bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):]
[:REAL,(BoundedLinearOperators (X,X)):] is V15() set
[:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is V15() set
bool [:[:REAL,(BoundedLinearOperators (X,X)):],(BoundedLinearOperators (X,X)):] is set
(X) is Element of BoundedLinearOperators (X,X)
id the carrier of X is non empty V15() V18( the carrier of X) V19( the carrier of X) Function-like one-to-one V25( the carrier of X) V29( the carrier of X, the carrier of X) Element of bool [: the carrier of X, the carrier of X:]
Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X))) is Element of BoundedLinearOperators (X,X)
BoundedLinearOperatorsNorm (X,X) is non empty V15() Function-like V25( BoundedLinearOperators (X,X)) V29( BoundedLinearOperators (X,X), REAL ) V36() V37() V38() Element of bool [:(BoundedLinearOperators (X,X)),REAL:]
[:(BoundedLinearOperators (X,X)),REAL:] is V15() V36() V37() V38() set
bool [:(BoundedLinearOperators (X,X)),REAL:] is set
((BoundedLinearOperators (X,X)),(X),(Add_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(Mult_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(X),(Zero_ ((BoundedLinearOperators (X,X)),(R_VectorSpace_of_LinearOperators (X,X)))),(BoundedLinearOperatorsNorm (X,X))) is () ()
1. (X) is left_complementable right_complementable complementable Element of the carrier of (X)
the carrier of (X) is non empty set
the OneF of (X) is left_complementable right_complementable complementable Element of the carrier of (X)