REAL is non empty V38() V39() V40() V44() V55() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V38() V39() V40() V41() V42() V43() V44() Element of bool REAL
bool REAL is non empty set
COMPLEX is non empty V38() V44() V55() set
omega is non empty epsilon-transitive epsilon-connected ordinal V38() V39() V40() V41() V42() V43() V44() set
bool omega is non empty set
bool NAT is non empty set
[:NAT,REAL:] is non empty set
bool [:NAT,REAL:] is non empty set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V33() real ext-real non positive non negative V38() V39() V40() V41() V42() V43() V44() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V33() real ext-real positive non negative V38() V39() V40() V41() V42() V43() Element of NAT
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V33() real ext-real non positive non negative V38() V39() V40() V41() V42() V43() V44() Element of NAT
sqrt 0 is V33() real ext-real Element of REAL
- 1 is V33() real ext-real non positive Element of REAL
4 is non empty epsilon-transitive epsilon-connected ordinal natural V33() real ext-real positive non negative V38() V39() V40() V41() V42() V43() Element of NAT
the non empty set is non empty set
the Element of the non empty set is Element of the non empty set
[: the non empty set , the non empty set :] is non empty set
[:[: the non empty set , the non empty set :], the non empty set :] is non empty set
bool [:[: the non empty set , the non empty set :], the non empty set :] is non empty set
the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued Function-like non empty total V18([: 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 Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued Function-like non empty total V18([: 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 non empty set
[:[:REAL, the non empty set :], the non empty set :] is non empty set
bool [:[:REAL, the non empty set :], the non empty set :] is non empty set
the Relation-like [:REAL, the non empty set :] -defined the non empty set -valued Function-like non empty total V18([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, the non empty set :], the non empty set :] is Relation-like [:REAL, the non empty set :] -defined the non empty set -valued Function-like non empty total V18([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, the non empty set :], the non empty set :]
[:[: the non empty set , the non empty set :],REAL:] is non empty set
bool [:[: the non empty set , the non empty set :],REAL:] is non empty set
the Relation-like [: the non empty set , the non empty set :] -defined REAL -valued Function-like non empty total V18([: the non empty set , the non empty set :], REAL ) Element of bool [:[: the non empty set , the non empty set :],REAL:] is Relation-like [: the non empty set , the non empty set :] -defined REAL -valued Function-like non empty total V18([: the non empty set , the non empty set :], REAL ) Element of bool [:[: the non empty set , the non empty set :],REAL:]
( the non empty set , the Element of the non empty set , the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued Function-like non empty total V18([: 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 Relation-like [:REAL, the non empty set :] -defined the non empty set -valued Function-like non empty total V18([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, the non empty set :], the non empty set :], the Relation-like [: the non empty set , the non empty set :] -defined REAL -valued Function-like non empty total V18([: the non empty set , the non empty set :], REAL ) Element of bool [:[: the non empty set , the non empty set :],REAL:]) is () ()
the carrier of ( the non empty set , the Element of the non empty set , the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued Function-like non empty total V18([: 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 Relation-like [:REAL, the non empty set :] -defined the non empty set -valued Function-like non empty total V18([:REAL, the non empty set :], the non empty set ) Element of bool [:[:REAL, the non empty set :], the non empty set :], the Relation-like [: the non empty set , the non empty set :] -defined REAL -valued Function-like non empty total V18([: the non empty set , the non empty set :], REAL ) Element of bool [:[: the non empty set , the non empty set :],REAL:]) is set
V0 is non empty set
[:V0,V0:] is non empty set
[:[:V0,V0:],V0:] is non empty set
bool [:[:V0,V0:],V0:] is non empty set
[:REAL,V0:] is non empty set
[:[:REAL,V0:],V0:] is non empty set
bool [:[:REAL,V0:],V0:] is non empty set
[:[:V0,V0:],REAL:] is non empty set
bool [:[:V0,V0:],REAL:] is non empty set
nilfunc is Element of V0
X0 is Relation-like [:V0,V0:] -defined V0 -valued Function-like non empty total V18([:V0,V0:],V0) Element of bool [:[:V0,V0:],V0:]
a is Relation-like [:REAL,V0:] -defined V0 -valued Function-like non empty total V18([:REAL,V0:],V0) Element of bool [:[:REAL,V0:],V0:]
X is Relation-like [:V0,V0:] -defined REAL -valued Function-like non empty total V18([:V0,V0:], REAL ) Element of bool [:[:V0,V0:],REAL:]
(V0,nilfunc,X0,a,X) is () ()
V0 is non empty ()
the carrier of V0 is non empty set
[: the carrier of V0, the carrier of V0:] is non empty set
the of V0 is Relation-like [: the carrier of V0, the carrier of V0:] -defined REAL -valued Function-like non empty total V18([: the carrier of V0, the carrier of V0:], REAL ) Element of bool [:[: the carrier of V0, the carrier of V0:],REAL:]
[:[: the carrier of V0, the carrier of V0:],REAL:] is non empty set
bool [:[: the carrier of V0, the carrier of V0:],REAL:] is non empty set
nilfunc is Element of the carrier of V0
X0 is Element of the carrier of V0
[nilfunc,X0] is Element of [: the carrier of V0, the carrier of V0:]
the of V0 . [nilfunc,X0] is V33() real ext-real Element of REAL
the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
(0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct is non empty right_complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is non empty set
the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct is non empty set
0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct is V74( the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) right_complementable Element of the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
the ZeroF of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct is right_complementable Element of the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
{(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )} is non empty Element of bool the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct
bool the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct is non empty set
[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):],REAL:] is non empty set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):],REAL:] is non empty set
[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] --> 0 is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] -defined NAT -valued Function-like non empty total V18([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], NAT ) Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):],NAT:]
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):],NAT:] is non empty set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):],NAT:] is non empty set
nilfunc is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] -defined REAL -valued Function-like non empty total V18([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], REAL ) Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):],REAL:]
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
[X0,a] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [X0,a] is V33() real ext-real Element of REAL
[(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )] is Element of [: the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct , the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct :]
[: the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct , the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct :] is non empty set
nilfunc . [(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )] is set
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
[X0,a] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [X0,a] is V33() real ext-real Element of REAL
[a,X0] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [a,X0] is V33() real ext-real Element of REAL
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
X0 + a is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) -valued Function-like non empty total V18([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )) Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (X0,a) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
X is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
[(X0 + a),X] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [(X0 + a),X] is V33() real ext-real Element of REAL
[X0,X] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [X0,X] is V33() real ext-real Element of REAL
[a,X] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [a,X] is V33() real ext-real Element of REAL
(nilfunc . [X0,X]) + (nilfunc . [a,X]) is V33() real ext-real Element of REAL
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
[X0,a] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [X0,a] is V33() real ext-real Element of REAL
X is V33() real ext-real Element of REAL
X * X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is Relation-like [:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) -valued Function-like non empty total V18([:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )) Element of bool [:[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
[:[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
bool [:[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (X,X0) is set
[(X * X0),a] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [(X * X0),a] is V33() real ext-real Element of REAL
X * (nilfunc . [X0,a]) is V33() real ext-real Element of REAL
0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is V74( (0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the ZeroF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) -valued Function-like non empty total V18([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )) Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) is Relation-like [:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) -valued Function-like non empty total V18([:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )) Element of bool [:[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
[:[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
bool [:[:REAL, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):] is non empty set
( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is non empty () ()
the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is non empty set
0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is V74(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)) Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the ZeroF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),a,a) is V33() real ext-real Element of REAL
[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is Relation-like [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] -defined REAL -valued Function-like non empty total V18([: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], REAL ) Element of bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):],REAL:]
[:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):],REAL:] is non empty set
bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):],REAL:] is non empty set
[a,a] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [a,a] is V33() real ext-real Element of REAL
X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),a,X) is V33() real ext-real Element of REAL
[a,X] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [a,X] is V33() real ext-real Element of REAL
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),X,a) is V33() real ext-real Element of REAL
[X,a] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [X,a] is V33() real ext-real Element of REAL
a + X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is Relation-like [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] -defined the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) -valued Function-like non empty total V18([: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)) Element of bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
[:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] is non empty set
bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,X) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),(a + X),seq1) is V33() real ext-real Element of REAL
[(a + X),seq1] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [(a + X),seq1] is V33() real ext-real Element of REAL
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),a,seq1) is V33() real ext-real Element of REAL
[a,seq1] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [a,seq1] is V33() real ext-real Element of REAL
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [X,seq1] is V33() real ext-real Element of REAL
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),a,seq1) + (( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),X,seq1) is V33() real ext-real Element of REAL
n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
z is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
n + z is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (n,z) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
[(n + z),n] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [(n + z),n] is V33() real ext-real Element of REAL
seq2 is V33() real ext-real Element of REAL
seq2 * a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) is Relation-like [:REAL, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] -defined the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) -valued Function-like non empty total V18([:REAL, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)) Element of bool [:[:REAL, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
[:REAL, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] is non empty set
[:[:REAL, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] is non empty set
bool [:[:REAL, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):] is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (seq2,a) is set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),(seq2 * a),X) is V33() real ext-real Element of REAL
[(seq2 * a),X] is Element of [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc):]
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . [(seq2 * a),X] is V33() real ext-real Element of REAL
seq2 * (( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc),a,X) is V33() real ext-real Element of REAL
n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq2 * n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (seq2,n) is set
z is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
[(seq2 * n),z] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ):]
nilfunc . [(seq2 * n),z] is V33() real ext-real Element of REAL
a is V33() real ext-real set
X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X + seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (X,seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a * (X + seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,(X + seq1)) is set
a * X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,X) is set
a * seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,seq1) is set
(a * X) + (a * seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . ((a * X),(a * seq1)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq2 + n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (seq2,n) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a * (seq2 + n) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (a,(seq2 + n)) is set
a * seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (a,seq2) is set
a * n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (a,n) is set
(a * seq2) + (a * n) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . ((a * seq2),(a * n)) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is V33() real ext-real set
X is V33() real ext-real set
a + X is V33() real ext-real set
seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
(a + X) * seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . ((a + X),seq1) is set
a * seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,seq1) is set
X * seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (X,seq1) is set
(a * seq1) + (X * seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . ((a * seq1),(X * seq1)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
(a + X) * seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . ((a + X),seq2) is set
a * seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (a,seq2) is set
X * seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (X,seq2) is set
(a * seq2) + (X * seq2) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . ((a * seq2),(X * seq2)) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is V33() real ext-real set
X is V33() real ext-real set
a * X is V33() real ext-real set
seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
(a * X) * seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . ((a * X),seq1) is set
X * seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (X,seq1) is set
a * (X * seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,(X * seq1)) is set
seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
(a * X) * seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . ((a * X),seq2) is set
X * seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (X,seq2) is set
a * (X * seq2) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (a,(X * seq2)) is set
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
1 * a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (1,a) is set
X is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
1 * X is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (1,X) is set
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a + X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,X) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq1 + seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (seq1,seq2) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
n is V33() real ext-real Element of REAL
n * a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (n,a) is set
n * seq1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (n,seq1) is set
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a + X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,X) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X + a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (X,a) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq2 + seq1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (seq2,seq1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a + X is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,X) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
(a + X) + seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . ((a + X),seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X + seq1 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (X,seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a + (X + seq1) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,(X + seq1)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
seq2 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq2 + n is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (seq2,n) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
z is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
(seq2 + n) + z is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . ((seq2 + n),z) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
n + z is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (n,z) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq2 + (n + z) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (seq2,(n + z)) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a + (0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,(0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc))) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
X + (0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (X,(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ))) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
a is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
X is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
X + seq1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ) . (X,seq1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )
seq2 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a + seq2 is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc) . (a,seq2) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital RLSStruct ),nilfunc)
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
seq2 is right_complementable Element of the carrier of a
n is right_complementable Element of the carrier of a
(a,seq2,n) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[seq2,n] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq2,n] is V33() real ext-real Element of REAL
(a,n,seq2) is V33() real ext-real Element of REAL
[n,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [n,seq2] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
0. a is V74(a) right_complementable Element of the carrier of a
the carrier of a is non empty set
the ZeroF of a is right_complementable Element of the carrier of a
(a,(0. a),(0. a)) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(0. a),(0. a)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(0. a),(0. a)] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
seq2 is right_complementable Element of the carrier of a
seq1 + seq2 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (seq1,seq2) is right_complementable Element of the carrier of a
(a,X,(seq1 + seq2)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,(seq1 + seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(seq1 + seq2)] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
(a,X,seq2) is V33() real ext-real Element of REAL
[X,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq2] is V33() real ext-real Element of REAL
(a,X,seq1) + (a,X,seq2) is V33() real ext-real Element of REAL
X is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of X is non empty set
seq1 is right_complementable Element of the carrier of X
seq2 is right_complementable Element of the carrier of X
a is V33() real ext-real Element of REAL
a * seq2 is right_complementable Element of the carrier of X
the Mult of X is Relation-like [:REAL, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: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 non empty set
[:[:REAL, the carrier of X:], the carrier of X:] is non empty set
bool [:[:REAL, the carrier of X:], the carrier of X:] is non empty set
the Mult of X . (a,seq2) is set
(X,seq1,(a * seq2)) is V33() real ext-real Element of REAL
[: the carrier of X, the carrier of X:] is non empty set
the of X is Relation-like [: the carrier of X, the carrier of X:] -defined REAL -valued Function-like non empty total V18([: the carrier of X, the carrier of X:], REAL ) Element of bool [:[: the carrier of X, the carrier of X:],REAL:]
[:[: the carrier of X, the carrier of X:],REAL:] is non empty set
bool [:[: the carrier of X, the carrier of X:],REAL:] is non empty set
[seq1,(a * seq2)] is Element of [: the carrier of X, the carrier of X:]
the of X . [seq1,(a * seq2)] is V33() real ext-real Element of REAL
(X,seq1,seq2) is V33() real ext-real Element of REAL
[seq1,seq2] is Element of [: the carrier of X, the carrier of X:]
the of X . [seq1,seq2] is V33() real ext-real Element of REAL
a * (X,seq1,seq2) is V33() real ext-real Element of REAL
a is V33() real ext-real Element of REAL
X is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of X is non empty set
seq1 is right_complementable Element of the carrier of X
a * seq1 is right_complementable Element of the carrier of X
the Mult of X is Relation-like [:REAL, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: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 non empty set
[:[:REAL, the carrier of X:], the carrier of X:] is non empty set
bool [:[:REAL, the carrier of X:], the carrier of X:] is non empty set
the Mult of X . (a,seq1) is set
seq2 is right_complementable Element of the carrier of X
(X,(a * seq1),seq2) is V33() real ext-real Element of REAL
[: the carrier of X, the carrier of X:] is non empty set
the of X is Relation-like [: the carrier of X, the carrier of X:] -defined REAL -valued Function-like non empty total V18([: the carrier of X, the carrier of X:], REAL ) Element of bool [:[: the carrier of X, the carrier of X:],REAL:]
[:[: the carrier of X, the carrier of X:],REAL:] is non empty set
bool [:[: the carrier of X, the carrier of X:],REAL:] is non empty set
[(a * seq1),seq2] is Element of [: the carrier of X, the carrier of X:]
the of X . [(a * seq1),seq2] is V33() real ext-real Element of REAL
a * seq2 is right_complementable Element of the carrier of X
the Mult of X . (a,seq2) is set
(X,seq1,(a * seq2)) is V33() real ext-real Element of REAL
[seq1,(a * seq2)] is Element of [: the carrier of X, the carrier of X:]
the of X . [seq1,(a * seq2)] is V33() real ext-real Element of REAL
(X,seq1,seq2) is V33() real ext-real Element of REAL
[seq1,seq2] is Element of [: the carrier of X, the carrier of X:]
the of X . [seq1,seq2] is V33() real ext-real Element of REAL
a * (X,seq1,seq2) is V33() real ext-real Element of REAL
a is V33() real ext-real Element of REAL
X is V33() real ext-real Element of REAL
seq1 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq1 is non empty set
seq2 is right_complementable Element of the carrier of seq1
a * seq2 is right_complementable Element of the carrier of seq1
the Mult of seq1 is Relation-like [:REAL, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([:REAL, the carrier of seq1:], the carrier of seq1) Element of bool [:[:REAL, the carrier of seq1:], the carrier of seq1:]
[:REAL, the carrier of seq1:] is non empty set
[:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
the Mult of seq1 . (a,seq2) is set
n is right_complementable Element of the carrier of seq1
X * n is right_complementable Element of the carrier of seq1
the Mult of seq1 . (X,n) is set
(a * seq2) + (X * n) is right_complementable Element of the carrier of seq1
the addF of seq1 is Relation-like [: the carrier of seq1, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([: the carrier of seq1, the carrier of seq1:], the carrier of seq1) Element of bool [:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:]
[: the carrier of seq1, the carrier of seq1:] is non empty set
[:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:] is non empty set
the addF of seq1 . ((a * seq2),(X * n)) is right_complementable Element of the carrier of seq1
z is right_complementable Element of the carrier of seq1
(seq1,((a * seq2) + (X * n)),z) is V33() real ext-real Element of REAL
the of seq1 is Relation-like [: the carrier of seq1, the carrier of seq1:] -defined REAL -valued Function-like non empty total V18([: the carrier of seq1, the carrier of seq1:], REAL ) Element of bool [:[: the carrier of seq1, the carrier of seq1:],REAL:]
[:[: the carrier of seq1, the carrier of seq1:],REAL:] is non empty set
bool [:[: the carrier of seq1, the carrier of seq1:],REAL:] is non empty set
[((a * seq2) + (X * n)),z] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [((a * seq2) + (X * n)),z] is V33() real ext-real Element of REAL
(seq1,seq2,z) is V33() real ext-real Element of REAL
[seq2,z] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [seq2,z] is V33() real ext-real Element of REAL
a * (seq1,seq2,z) is V33() real ext-real Element of REAL
(seq1,n,z) is V33() real ext-real Element of REAL
[n,z] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [n,z] is V33() real ext-real Element of REAL
X * (seq1,n,z) is V33() real ext-real Element of REAL
(a * (seq1,seq2,z)) + (X * (seq1,n,z)) is V33() real ext-real Element of REAL
(seq1,(a * seq2),z) is V33() real ext-real Element of REAL
[(a * seq2),z] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [(a * seq2),z] is V33() real ext-real Element of REAL
(seq1,(X * n),z) is V33() real ext-real Element of REAL
[(X * n),z] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [(X * n),z] is V33() real ext-real Element of REAL
(seq1,(a * seq2),z) + (seq1,(X * n),z) is V33() real ext-real Element of REAL
(a * (seq1,seq2,z)) + (seq1,(X * n),z) is V33() real ext-real Element of REAL
seq1 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq1 is non empty set
seq2 is right_complementable Element of the carrier of seq1
n is right_complementable Element of the carrier of seq1
a is V33() real ext-real Element of REAL
a * n is right_complementable Element of the carrier of seq1
the Mult of seq1 is Relation-like [:REAL, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([:REAL, the carrier of seq1:], the carrier of seq1) Element of bool [:[:REAL, the carrier of seq1:], the carrier of seq1:]
[:REAL, the carrier of seq1:] is non empty set
[:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
the Mult of seq1 . (a,n) is set
z is right_complementable Element of the carrier of seq1
X is V33() real ext-real Element of REAL
X * z is right_complementable Element of the carrier of seq1
the Mult of seq1 . (X,z) is set
(a * n) + (X * z) is right_complementable Element of the carrier of seq1
the addF of seq1 is Relation-like [: the carrier of seq1, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([: the carrier of seq1, the carrier of seq1:], the carrier of seq1) Element of bool [:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:]
[: the carrier of seq1, the carrier of seq1:] is non empty set
[:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:] is non empty set
the addF of seq1 . ((a * n),(X * z)) is right_complementable Element of the carrier of seq1
(seq1,seq2,((a * n) + (X * z))) is V33() real ext-real Element of REAL
the of seq1 is Relation-like [: the carrier of seq1, the carrier of seq1:] -defined REAL -valued Function-like non empty total V18([: the carrier of seq1, the carrier of seq1:], REAL ) Element of bool [:[: the carrier of seq1, the carrier of seq1:],REAL:]
[:[: the carrier of seq1, the carrier of seq1:],REAL:] is non empty set
bool [:[: the carrier of seq1, the carrier of seq1:],REAL:] is non empty set
[seq2,((a * n) + (X * z))] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [seq2,((a * n) + (X * z))] is V33() real ext-real Element of REAL
(seq1,seq2,n) is V33() real ext-real Element of REAL
[seq2,n] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [seq2,n] is V33() real ext-real Element of REAL
a * (seq1,seq2,n) is V33() real ext-real Element of REAL
(seq1,seq2,z) is V33() real ext-real Element of REAL
[seq2,z] is Element of [: the carrier of seq1, the carrier of seq1:]
the of seq1 . [seq2,z] is V33() real ext-real Element of REAL
X * (seq1,seq2,z) is V33() real ext-real Element of REAL
(a * (seq1,seq2,n)) + (X * (seq1,seq2,z)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,(- X),seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(- X),seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),seq1] is V33() real ext-real Element of REAL
- seq1 is right_complementable Element of the carrier of a
(a,X,(- seq1)) is V33() real ext-real Element of REAL
[X,(- seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(- seq1)] is V33() real ext-real Element of REAL
(- 1) * X is right_complementable Element of the carrier of a
the Mult of a is Relation-like [:REAL, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([:REAL, the carrier of a:], the carrier of a) Element of bool [:[:REAL, the carrier of a:], the carrier of a:]
[:REAL, the carrier of a:] is non empty set
[:[:REAL, the carrier of a:], the carrier of a:] is non empty set
bool [:[:REAL, the carrier of a:], the carrier of a:] is non empty set
the Mult of a . ((- 1),X) is set
(a,((- 1) * X),seq1) is V33() real ext-real Element of REAL
[((- 1) * X),seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [((- 1) * X),seq1] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
(- 1) * (a,X,seq1) is V33() real ext-real Element of REAL
(- 1) * seq1 is right_complementable Element of the carrier of a
the Mult of a . ((- 1),seq1) is set
(a,X,((- 1) * seq1)) is V33() real ext-real Element of REAL
[X,((- 1) * seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,((- 1) * seq1)] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,(- X),seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(- X),seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),seq1] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
- (a,X,seq1) is V33() real ext-real Element of REAL
(- 1) * X is right_complementable Element of the carrier of a
the Mult of a is Relation-like [:REAL, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([:REAL, the carrier of a:], the carrier of a) Element of bool [:[:REAL, the carrier of a:], the carrier of a:]
[:REAL, the carrier of a:] is non empty set
[:[:REAL, the carrier of a:], the carrier of a:] is non empty set
bool [:[:REAL, the carrier of a:], the carrier of a:] is non empty set
the Mult of a . ((- 1),X) is set
(a,((- 1) * X),seq1) is V33() real ext-real Element of REAL
[((- 1) * X),seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [((- 1) * X),seq1] is V33() real ext-real Element of REAL
(- 1) * (a,X,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
(a,X,(- seq1)) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,(- seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(- seq1)] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
- (a,X,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
(a,(- X),(- seq1)) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(- X),(- seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),(- seq1)] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
(a,X,(- seq1)) is V33() real ext-real Element of REAL
[X,(- seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(- seq1)] is V33() real ext-real Element of REAL
- (a,X,(- seq1)) is V33() real ext-real Element of REAL
- (a,X,seq1) is V33() real ext-real Element of REAL
- (- (a,X,seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
seq2 is right_complementable Element of the carrier of a
(a,(X - seq1),seq2) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),seq2] is V33() real ext-real Element of REAL
(a,X,seq2) is V33() real ext-real Element of REAL
[X,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq2] is V33() real ext-real Element of REAL
(a,seq1,seq2) is V33() real ext-real Element of REAL
[seq1,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq2] is V33() real ext-real Element of REAL
(a,X,seq2) - (a,seq1,seq2) is V33() real ext-real Element of REAL
(a,(- seq1),seq2) is V33() real ext-real Element of REAL
[(- seq1),seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- seq1),seq2] is V33() real ext-real Element of REAL
(a,X,seq2) + (a,(- seq1),seq2) is V33() real ext-real Element of REAL
- (a,seq1,seq2) is V33() real ext-real Element of REAL
(a,X,seq2) + (- (a,seq1,seq2)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
seq2 is right_complementable Element of the carrier of a
seq1 - seq2 is right_complementable Element of the carrier of a
- seq2 is right_complementable Element of the carrier of a
seq1 + (- seq2) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (seq1,(- seq2)) is right_complementable Element of the carrier of a
(a,X,(seq1 - seq2)) is V33() real ext-real Element of REAL
[X,(seq1 - seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(seq1 - seq2)] is V33() real ext-real Element of REAL
(a,X,seq2) is V33() real ext-real Element of REAL
[X,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq2] is V33() real ext-real Element of REAL
(a,X,seq1) - (a,X,seq2) is V33() real ext-real Element of REAL
(a,X,(- seq2)) is V33() real ext-real Element of REAL
[X,(- seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(- seq2)] is V33() real ext-real Element of REAL
(a,X,seq1) + (a,X,(- seq2)) is V33() real ext-real Element of REAL
- (a,X,seq2) is V33() real ext-real Element of REAL
(a,X,seq1) + (- (a,X,seq2)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
seq2 is right_complementable Element of the carrier of a
(a,X,seq2) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq2] is V33() real ext-real Element of REAL
(a,seq1,seq2) is V33() real ext-real Element of REAL
[seq1,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq2] is V33() real ext-real Element of REAL
n is right_complementable Element of the carrier of a
seq2 - n is right_complementable Element of the carrier of a
- n is right_complementable Element of the carrier of a
seq2 + (- n) is right_complementable Element of the carrier of a
the addF of a . (seq2,(- n)) is right_complementable Element of the carrier of a
(a,(X - seq1),(seq2 - n)) is V33() real ext-real Element of REAL
[(X - seq1),(seq2 - n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(seq2 - n)] is V33() real ext-real Element of REAL
(a,X,n) is V33() real ext-real Element of REAL
[X,n] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,n] is V33() real ext-real Element of REAL
(a,X,seq2) - (a,X,n) is V33() real ext-real Element of REAL
((a,X,seq2) - (a,X,n)) - (a,seq1,seq2) is V33() real ext-real Element of REAL
(a,seq1,n) is V33() real ext-real Element of REAL
[seq1,n] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,n] is V33() real ext-real Element of REAL
(((a,X,seq2) - (a,X,n)) - (a,seq1,seq2)) + (a,seq1,n) is V33() real ext-real Element of REAL
(a,X,(seq2 - n)) is V33() real ext-real Element of REAL
[X,(seq2 - n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(seq2 - n)] is V33() real ext-real Element of REAL
(a,seq1,(seq2 - n)) is V33() real ext-real Element of REAL
[seq1,(seq2 - n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,(seq2 - n)] is V33() real ext-real Element of REAL
(a,X,(seq2 - n)) - (a,seq1,(seq2 - n)) is V33() real ext-real Element of REAL
((a,X,seq2) - (a,X,n)) - (a,seq1,(seq2 - n)) is V33() real ext-real Element of REAL
(a,seq1,seq2) - (a,seq1,n) is V33() real ext-real Element of REAL
((a,X,seq2) - (a,X,n)) - ((a,seq1,seq2) - (a,seq1,n)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
X is right_complementable Element of the carrier of a
(a,(0. a),X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(0. a),X] is Element of [: the carrier of a, the carrier of a:]
the of a . [(0. a),X] is V33() real ext-real Element of REAL
(a,H1(a),X) is V33() real ext-real Element of REAL
- X is right_complementable Element of the carrier of a
X + (- X) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- X)) is right_complementable Element of the carrier of a
(a,(X + (- X)),X) is V33() real ext-real Element of REAL
[(X + (- X)),X] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X + (- X)),X] is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
(a,(- X),X) is V33() real ext-real Element of REAL
[(- X),X] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),X] is V33() real ext-real Element of REAL
(a,X,X) + (a,(- X),X) is V33() real ext-real Element of REAL
- (a,X,X) is V33() real ext-real Element of REAL
(a,X,X) + (- (a,X,X)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
(a,X,(0. a)) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,(0. a)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(0. a)] is V33() real ext-real Element of REAL
2 is non empty epsilon-transitive epsilon-connected ordinal natural V33() real ext-real positive non negative V38() V39() V40() V41() V42() V43() Element of NAT
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
X + seq1 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,seq1) is right_complementable Element of the carrier of a
(a,(X + seq1),(X + seq1)) is V33() real ext-real Element of REAL
[(X + seq1),(X + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X + seq1),(X + seq1)] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
2 * (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) + (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
((a,X,X) + (2 * (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X,(X + seq1)) is V33() real ext-real Element of REAL
[X,(X + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(X + seq1)] is V33() real ext-real Element of REAL
(a,seq1,(X + seq1)) is V33() real ext-real Element of REAL
[seq1,(X + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,(X + seq1)] is V33() real ext-real Element of REAL
(a,X,(X + seq1)) + (a,seq1,(X + seq1)) is V33() real ext-real Element of REAL
(a,X,X) + (a,X,seq1) is V33() real ext-real Element of REAL
((a,X,X) + (a,X,seq1)) + (a,seq1,(X + seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) + (a,seq1,seq1) is V33() real ext-real Element of REAL
((a,X,X) + (a,X,seq1)) + ((a,X,seq1) + (a,seq1,seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) + (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) + ((a,X,seq1) + (a,X,seq1)) is V33() real ext-real Element of REAL
((a,X,X) + ((a,X,seq1) + (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
X + seq1 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,seq1) is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X + seq1),(X - seq1)) is V33() real ext-real Element of REAL
[(X + seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X + seq1),(X - seq1)] is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
(a,X,X) - (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X,(X - seq1)) is V33() real ext-real Element of REAL
[X,(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(X - seq1)] is V33() real ext-real Element of REAL
(a,seq1,(X - seq1)) is V33() real ext-real Element of REAL
[seq1,(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,(X - seq1)] is V33() real ext-real Element of REAL
(a,X,(X - seq1)) + (a,seq1,(X - seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
(a,X,X) - (a,X,seq1) is V33() real ext-real Element of REAL
((a,X,X) - (a,X,seq1)) + (a,seq1,(X - seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) - (a,seq1,seq1) is V33() real ext-real Element of REAL
((a,X,X) - (a,X,seq1)) + ((a,X,seq1) - (a,seq1,seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
2 * (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) - (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
((a,X,X) - (2 * (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X,(X - seq1)) is V33() real ext-real Element of REAL
[X,(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(X - seq1)] is V33() real ext-real Element of REAL
(a,seq1,(X - seq1)) is V33() real ext-real Element of REAL
[seq1,(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,(X - seq1)] is V33() real ext-real Element of REAL
(a,X,(X - seq1)) - (a,seq1,(X - seq1)) is V33() real ext-real Element of REAL
(a,X,X) - (a,X,seq1) is V33() real ext-real Element of REAL
((a,X,X) - (a,X,seq1)) - (a,seq1,(X - seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) - (a,seq1,seq1) is V33() real ext-real Element of REAL
((a,X,X) - (a,X,seq1)) - ((a,X,seq1) - (a,seq1,seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) + (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) - ((a,X,seq1) + (a,X,seq1)) is V33() real ext-real Element of REAL
((a,X,X) - ((a,X,seq1) + (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
abs (a,X,seq1) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
sqrt (a,seq1,seq1) is V33() real ext-real Element of REAL
(sqrt (a,X,X)) * (sqrt (a,seq1,seq1)) is V33() real ext-real Element of REAL
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
2 * (a,X,seq1) is V33() real ext-real Element of REAL
seq2 is V33() real ext-real set
seq2 ^2 is V33() real ext-real set
seq2 * seq2 is V33() real ext-real set
(a,X,X) * (seq2 ^2) is V33() real ext-real Element of REAL
(2 * (a,X,seq1)) * seq2 is V33() real ext-real Element of REAL
((a,X,X) * (seq2 ^2)) + ((2 * (a,X,seq1)) * seq2) is V33() real ext-real Element of REAL
(((a,X,X) * (seq2 ^2)) + ((2 * (a,X,seq1)) * seq2)) + (a,seq1,seq1) is V33() real ext-real Element of REAL
n is V33() real ext-real Element of REAL
n * X is right_complementable Element of the carrier of a
the Mult of a is Relation-like [:REAL, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([:REAL, the carrier of a:], the carrier of a) Element of bool [:[:REAL, the carrier of a:], the carrier of a:]
[:REAL, the carrier of a:] is non empty set
[:[:REAL, the carrier of a:], the carrier of a:] is non empty set
bool [:[:REAL, the carrier of a:], the carrier of a:] is non empty set
the Mult of a . (n,X) is set
(n * X) + seq1 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((n * X),seq1) is right_complementable Element of the carrier of a
(a,((n * X) + seq1),((n * X) + seq1)) is V33() real ext-real Element of REAL
[((n * X) + seq1),((n * X) + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [((n * X) + seq1),((n * X) + seq1)] is V33() real ext-real Element of REAL
(a,(n * X),(n * X)) is V33() real ext-real Element of REAL
[(n * X),(n * X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(n * X),(n * X)] is V33() real ext-real Element of REAL
(a,(n * X),seq1) is V33() real ext-real Element of REAL
[(n * X),seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [(n * X),seq1] is V33() real ext-real Element of REAL
2 * (a,(n * X),seq1) is V33() real ext-real Element of REAL
(a,(n * X),(n * X)) + (2 * (a,(n * X),seq1)) is V33() real ext-real Element of REAL
((a,(n * X),(n * X)) + (2 * (a,(n * X),seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X,(n * X)) is V33() real ext-real Element of REAL
[X,(n * X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(n * X)] is V33() real ext-real Element of REAL
n * (a,X,(n * X)) is V33() real ext-real Element of REAL
(n * (a,X,(n * X))) + (2 * (a,(n * X),seq1)) is V33() real ext-real Element of REAL
((n * (a,X,(n * X))) + (2 * (a,(n * X),seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
n * (a,X,X) is V33() real ext-real Element of REAL
n * (n * (a,X,X)) is V33() real ext-real Element of REAL
(n * (n * (a,X,X))) + (2 * (a,(n * X),seq1)) is V33() real ext-real Element of REAL
((n * (n * (a,X,X))) + (2 * (a,(n * X),seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
n ^2 is V33() real ext-real Element of REAL
n * n is V33() real ext-real set
(a,X,X) * (n ^2) is V33() real ext-real Element of REAL
(a,X,seq1) * n is V33() real ext-real Element of REAL
2 * ((a,X,seq1) * n) is V33() real ext-real Element of REAL
((a,X,X) * (n ^2)) + (2 * ((a,X,seq1) * n)) is V33() real ext-real Element of REAL
(((a,X,X) * (n ^2)) + (2 * ((a,X,seq1) * n))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
delta ((a,X,X),(2 * (a,X,seq1)),(a,seq1,seq1)) is V33() real ext-real Element of REAL
(2 * (a,X,seq1)) ^2 is V33() real ext-real Element of REAL
(2 * (a,X,seq1)) * (2 * (a,X,seq1)) is V33() real ext-real set
4 * (a,X,X) is V33() real ext-real Element of REAL
(4 * (a,X,X)) * (a,seq1,seq1) is V33() real ext-real Element of REAL
((2 * (a,X,seq1)) ^2) - ((4 * (a,X,X)) * (a,seq1,seq1)) is V33() real ext-real Element of REAL
(a,X,seq1) ^2 is V33() real ext-real Element of REAL
(a,X,seq1) * (a,X,seq1) is V33() real ext-real set
(a,X,X) * (a,seq1,seq1) is V33() real ext-real Element of REAL
((a,X,seq1) ^2) - ((a,X,X) * (a,seq1,seq1)) is V33() real ext-real Element of REAL
4 * (((a,X,seq1) ^2) - ((a,X,X) * (a,seq1,seq1))) is V33() real ext-real Element of REAL
0 / 4 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V33() real ext-real non positive non negative V38() V39() V40() V41() V42() V43() V44() Element of REAL
(abs (a,X,seq1)) ^2 is V33() real ext-real Element of REAL
(abs (a,X,seq1)) * (abs (a,X,seq1)) is V33() real ext-real set
sqrt ((abs (a,X,seq1)) ^2) is V33() real ext-real Element of REAL
sqrt ((a,X,X) * (a,seq1,seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
seq2 is right_complementable Element of the carrier of a
n is right_complementable Element of the carrier of a
(a,seq2,n) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[seq2,n] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq2,n] is V33() real ext-real Element of REAL
(a,n,seq2) is V33() real ext-real Element of REAL
[n,seq2] is Element of [: the carrier of a, the carrier of a:]
the of a . [n,seq2] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
- (a,X,seq1) is V33() real ext-real Element of REAL
- 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V33() real ext-real non positive non negative V38() V39() V40() V41() V42() V43() V44() Element of REAL
(a,X,(- seq1)) is V33() real ext-real Element of REAL
[X,(- seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(- seq1)] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
- (a,X,seq1) is V33() real ext-real Element of REAL
- 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V33() real ext-real non positive non negative V38() V39() V40() V41() V42() V43() V44() Element of REAL
(a,(- X),seq1) is V33() real ext-real Element of REAL
[(- X),seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),seq1] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
(a,(- X),(- seq1)) is V33() real ext-real Element of REAL
[(- X),(- seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),(- seq1)] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
X is right_complementable Element of the carrier of a
(a,X,H1(a)) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,(0. a)] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,(0. a)] is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
X + seq1 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,seq1) is right_complementable Element of the carrier of a
(a,(X + seq1),(X + seq1)) is V33() real ext-real Element of REAL
[(X + seq1),(X + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X + seq1),(X + seq1)] is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
(a,X,X) + (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
2 * (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) + (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
((a,X,X) + (2 * (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
(a,X,X) + (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
2 * (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) - (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
((a,X,X) - (2 * (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
((a,X,X) + (a,seq1,seq1)) - 0 is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
X is right_complementable Element of the carrier of a
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
a is V33() real ext-real Element of REAL
abs a is V33() real ext-real Element of REAL
X is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of X is non empty set
seq1 is right_complementable Element of the carrier of X
a * seq1 is right_complementable Element of the carrier of X
the Mult of X is Relation-like [:REAL, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: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 non empty set
[:[:REAL, the carrier of X:], the carrier of X:] is non empty set
bool [:[:REAL, the carrier of X:], the carrier of X:] is non empty set
the Mult of X . (a,seq1) is set
(X,(a * seq1)) is V33() real ext-real Element of REAL
(X,(a * seq1),(a * seq1)) is V33() real ext-real Element of REAL
[: the carrier of X, the carrier of X:] is non empty set
the of X is Relation-like [: the carrier of X, the carrier of X:] -defined REAL -valued Function-like non empty total V18([: the carrier of X, the carrier of X:], REAL ) Element of bool [:[: the carrier of X, the carrier of X:],REAL:]
[:[: the carrier of X, the carrier of X:],REAL:] is non empty set
bool [:[: the carrier of X, the carrier of X:],REAL:] is non empty set
[(a * seq1),(a * seq1)] is Element of [: the carrier of X, the carrier of X:]
the of X . [(a * seq1),(a * seq1)] is V33() real ext-real Element of REAL
sqrt (X,(a * seq1),(a * seq1)) is V33() real ext-real Element of REAL
(X,seq1) is V33() real ext-real Element of REAL
(X,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of X, the carrier of X:]
the of X . [seq1,seq1] is V33() real ext-real Element of REAL
sqrt (X,seq1,seq1) is V33() real ext-real Element of REAL
(abs a) * (X,seq1) is V33() real ext-real Element of REAL
a ^2 is V33() real ext-real Element of REAL
a * a is V33() real ext-real set
(X,seq1,(a * seq1)) is V33() real ext-real Element of REAL
[seq1,(a * seq1)] is Element of [: the carrier of X, the carrier of X:]
the of X . [seq1,(a * seq1)] is V33() real ext-real Element of REAL
a * (X,seq1,(a * seq1)) is V33() real ext-real Element of REAL
sqrt (a * (X,seq1,(a * seq1))) is V33() real ext-real Element of REAL
a * (X,seq1,seq1) is V33() real ext-real Element of REAL
a * (a * (X,seq1,seq1)) is V33() real ext-real Element of REAL
sqrt (a * (a * (X,seq1,seq1))) is V33() real ext-real Element of REAL
(a ^2) * (X,seq1,seq1) is V33() real ext-real Element of REAL
sqrt ((a ^2) * (X,seq1,seq1)) is V33() real ext-real Element of REAL
sqrt (a ^2) is V33() real ext-real Element of REAL
(sqrt (a ^2)) * (sqrt (X,seq1,seq1)) is V33() real ext-real Element of REAL
(abs a) * (sqrt (X,seq1,seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
abs (a,X,seq1) is V33() real ext-real Element of REAL
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
(a,seq1) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
sqrt (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X) * (a,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
X + seq1 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,seq1) is right_complementable Element of the carrier of a
(a,(X + seq1)) is V33() real ext-real Element of REAL
(a,(X + seq1),(X + seq1)) is V33() real ext-real Element of REAL
[(X + seq1),(X + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X + seq1),(X + seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X + seq1),(X + seq1)) is V33() real ext-real Element of REAL
(a,seq1) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
sqrt (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X) + (a,seq1) is V33() real ext-real Element of REAL
(a,(X + seq1)) ^2 is V33() real ext-real Element of REAL
(a,(X + seq1)) * (a,(X + seq1)) is V33() real ext-real set
sqrt ((a,(X + seq1)) ^2) is V33() real ext-real Element of REAL
(a,X,seq1) is V33() real ext-real Element of REAL
[X,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,seq1] is V33() real ext-real Element of REAL
2 * (a,X,seq1) is V33() real ext-real Element of REAL
(a,X,X) + (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
((a,X,X) + (2 * (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
(sqrt (a,X,X)) ^2 is V33() real ext-real Element of REAL
(sqrt (a,X,X)) * (sqrt (a,X,X)) is V33() real ext-real set
((sqrt (a,X,X)) ^2) + (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
(((sqrt (a,X,X)) ^2) + (2 * (a,X,seq1))) + (a,seq1,seq1) is V33() real ext-real Element of REAL
abs (a,X,seq1) is V33() real ext-real Element of REAL
(a,X) * (a,seq1) is V33() real ext-real Element of REAL
2 * ((a,X) * (a,seq1)) is V33() real ext-real Element of REAL
(a,X) ^2 is V33() real ext-real Element of REAL
(a,X) * (a,X) is V33() real ext-real set
((a,X) ^2) + (2 * (a,X,seq1)) is V33() real ext-real Element of REAL
2 * (a,X) is V33() real ext-real Element of REAL
(2 * (a,X)) * (a,seq1) is V33() real ext-real Element of REAL
((a,X) ^2) + ((2 * (a,X)) * (a,seq1)) is V33() real ext-real Element of REAL
(a,seq1) ^2 is V33() real ext-real Element of REAL
(a,seq1) * (a,seq1) is V33() real ext-real set
(((a,X) ^2) + (2 * (a,X,seq1))) + ((a,seq1) ^2) is V33() real ext-real Element of REAL
(((a,X) ^2) + ((2 * (a,X)) * (a,seq1))) + ((a,seq1) ^2) is V33() real ext-real Element of REAL
((a,X) + (a,seq1)) ^2 is V33() real ext-real Element of REAL
((a,X) + (a,seq1)) * ((a,X) + (a,seq1)) is V33() real ext-real set
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
(a,(- X)) is V33() real ext-real Element of REAL
(a,(- X),(- X)) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(- X),(- X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- X),(- X)] is V33() real ext-real Element of REAL
sqrt (a,(- X),(- X)) is V33() real ext-real Element of REAL
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
abs (- 1) is V33() real ext-real Element of REAL
- (- 1) is V33() real ext-real non negative Element of REAL
(- 1) * X is right_complementable Element of the carrier of a
the Mult of a is Relation-like [:REAL, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([:REAL, the carrier of a:], the carrier of a) Element of bool [:[:REAL, the carrier of a:], the carrier of a:]
[:REAL, the carrier of a:] is non empty set
[:[:REAL, the carrier of a:], the carrier of a:] is non empty set
bool [:[:REAL, the carrier of a:], the carrier of a:] is non empty set
the Mult of a . ((- 1),X) is set
(a,((- 1) * X)) is V33() real ext-real Element of REAL
(a,((- 1) * X),((- 1) * X)) is V33() real ext-real Element of REAL
[((- 1) * X),((- 1) * X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [((- 1) * X),((- 1) * X)] is V33() real ext-real Element of REAL
sqrt (a,((- 1) * X),((- 1) * X)) is V33() real ext-real Element of REAL
1 * (a,X) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
(a,seq1) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
sqrt (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X) - (a,seq1) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
(X - seq1) + seq1 is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),seq1) is right_complementable Element of the carrier of a
seq1 - seq1 is right_complementable Element of the carrier of a
seq1 + (- seq1) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- seq1)) is right_complementable Element of the carrier of a
X - (seq1 - seq1) is right_complementable Element of the carrier of a
- (seq1 - seq1) is right_complementable Element of the carrier of a
X + (- (seq1 - seq1)) is right_complementable Element of the carrier of a
the addF of a . (X,(- (seq1 - seq1))) is right_complementable Element of the carrier of a
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
X - H1(a) is right_complementable Element of the carrier of a
- (0. a) is right_complementable Element of the carrier of a
X + (- (0. a)) is right_complementable Element of the carrier of a
the addF of a . (X,(- (0. a))) is right_complementable Element of the carrier of a
(a,(X - seq1)) + (a,seq1) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X) is V33() real ext-real Element of REAL
(a,X,X) is V33() real ext-real Element of REAL
[: the carrier of a, the carrier of a:] is non empty set
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[X,X] is Element of [: the carrier of a, the carrier of a:]
the of a . [X,X] is V33() real ext-real Element of REAL
sqrt (a,X,X) is V33() real ext-real Element of REAL
seq1 is right_complementable Element of the carrier of a
(a,seq1) is V33() real ext-real Element of REAL
(a,seq1,seq1) is V33() real ext-real Element of REAL
[seq1,seq1] is Element of [: the carrier of a, the carrier of a:]
the of a . [seq1,seq1] is V33() real ext-real Element of REAL
sqrt (a,seq1,seq1) is V33() real ext-real Element of REAL
(a,X) - (a,seq1) is V33() real ext-real Element of REAL
abs ((a,X) - (a,seq1)) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
seq1 - X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 + (- X) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- X)) is right_complementable Element of the carrier of a
(seq1 - X) + X is right_complementable Element of the carrier of a
the addF of a . ((seq1 - X),X) is right_complementable Element of the carrier of a
X - X is right_complementable Element of the carrier of a
X + (- X) is right_complementable Element of the carrier of a
the addF of a . (X,(- X)) is right_complementable Element of the carrier of a
seq1 - (X - X) is right_complementable Element of the carrier of a
- (X - X) is right_complementable Element of the carrier of a
seq1 + (- (X - X)) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- (X - X))) is right_complementable Element of the carrier of a
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
seq1 - H1(a) is right_complementable Element of the carrier of a
- (0. a) is right_complementable Element of the carrier of a
seq1 + (- (0. a)) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- (0. a))) is right_complementable Element of the carrier of a
(a,(seq1 - X)) is V33() real ext-real Element of REAL
(a,(seq1 - X),(seq1 - X)) is V33() real ext-real Element of REAL
[(seq1 - X),(seq1 - X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(seq1 - X),(seq1 - X)] is V33() real ext-real Element of REAL
sqrt (a,(seq1 - X),(seq1 - X)) is V33() real ext-real Element of REAL
(a,(seq1 - X)) + (a,X) is V33() real ext-real Element of REAL
(a,seq1) - (a,X) is V33() real ext-real Element of REAL
- (X - seq1) is right_complementable Element of the carrier of a
(a,(- (X - seq1))) is V33() real ext-real Element of REAL
(a,(- (X - seq1)),(- (X - seq1))) is V33() real ext-real Element of REAL
[(- (X - seq1)),(- (X - seq1))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- (X - seq1)),(- (X - seq1))] is V33() real ext-real Element of REAL
sqrt (a,(- (X - seq1)),(- (X - seq1))) is V33() real ext-real Element of REAL
- (a,(X - seq1)) is V33() real ext-real Element of REAL
- ((a,seq1) - (a,X)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
seq2 is V33() real ext-real Element of REAL
n is right_complementable Element of the carrier of a
z is right_complementable Element of the carrier of a
n - z is right_complementable Element of the carrier of a
- z is right_complementable Element of the carrier of a
n + (- z) is right_complementable Element of the carrier of a
the addF of a . (n,(- z)) is right_complementable Element of the carrier of a
(a,(n - z)) is V33() real ext-real Element of REAL
(a,(n - z),(n - z)) is V33() real ext-real Element of REAL
[(n - z),(n - z)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(n - z),(n - z)] is V33() real ext-real Element of REAL
sqrt (a,(n - z),(n - z)) is V33() real ext-real Element of REAL
z - n is right_complementable Element of the carrier of a
- n is right_complementable Element of the carrier of a
z + (- n) is right_complementable Element of the carrier of a
the addF of a . (z,(- n)) is right_complementable Element of the carrier of a
(a,(z - n)) is V33() real ext-real Element of REAL
(a,(z - n),(z - n)) is V33() real ext-real Element of REAL
[(z - n),(z - n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(z - n),(z - n)] is V33() real ext-real Element of REAL
sqrt (a,(z - n),(z - n)) is V33() real ext-real Element of REAL
- (z - n) is right_complementable Element of the carrier of a
(a,(- (z - n))) is V33() real ext-real Element of REAL
(a,(- (z - n)),(- (z - n))) is V33() real ext-real Element of REAL
[(- (z - n)),(- (z - n))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- (z - n)),(- (z - n))] is V33() real ext-real Element of REAL
sqrt (a,(- (z - n)),(- (z - n))) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
(a,X,X) is V33() real ext-real Element of REAL
X - X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
X + (- X) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- X)) is right_complementable Element of the carrier of a
(a,(X - X)) is V33() real ext-real Element of REAL
(a,(X - X),(X - X)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - X),(X - X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - X),(X - X)] is V33() real ext-real Element of REAL
sqrt (a,(X - X),(X - X)) is V33() real ext-real Element of REAL
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
(a,H1(a)) is V33() real ext-real Element of REAL
(a,(0. a),(0. a)) is V33() real ext-real Element of REAL
[(0. a),(0. a)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(0. a),(0. a)] is V33() real ext-real Element of REAL
sqrt (a,(0. a),(0. a)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
seq2 is right_complementable Element of the carrier of a
(a,X,seq2) is V33() real ext-real Element of REAL
X - seq2 is right_complementable Element of the carrier of a
- seq2 is right_complementable Element of the carrier of a
X + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (X,(- seq2)) is right_complementable Element of the carrier of a
(a,(X - seq2)) is V33() real ext-real Element of REAL
(a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
[(X - seq2),(X - seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq2),(X - seq2)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
(a,seq2,seq1) is V33() real ext-real Element of REAL
seq2 - seq1 is right_complementable Element of the carrier of a
seq2 + (- seq1) is right_complementable Element of the carrier of a
the addF of a . (seq2,(- seq1)) is right_complementable Element of the carrier of a
(a,(seq2 - seq1)) is V33() real ext-real Element of REAL
(a,(seq2 - seq1),(seq2 - seq1)) is V33() real ext-real Element of REAL
[(seq2 - seq1),(seq2 - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(seq2 - seq1),(seq2 - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(seq2 - seq1),(seq2 - seq1)) is V33() real ext-real Element of REAL
(a,X,seq2) + (a,seq2,seq1) is V33() real ext-real Element of REAL
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
(X - seq1) + H1(a) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(0. a)) is right_complementable Element of the carrier of a
(a,((X - seq1) + H1(a))) is V33() real ext-real Element of REAL
(a,((X - seq1) + H1(a)),((X - seq1) + H1(a))) is V33() real ext-real Element of REAL
[((X - seq1) + H1(a)),((X - seq1) + H1(a))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq1) + H1(a)),((X - seq1) + H1(a))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq1) + H1(a)),((X - seq1) + H1(a))) is V33() real ext-real Element of REAL
seq2 - seq2 is right_complementable Element of the carrier of a
seq2 + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (seq2,(- seq2)) is right_complementable Element of the carrier of a
(X - seq1) + (seq2 - seq2) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(seq2 - seq2)) is right_complementable Element of the carrier of a
(a,((X - seq1) + (seq2 - seq2))) is V33() real ext-real Element of REAL
(a,((X - seq1) + (seq2 - seq2)),((X - seq1) + (seq2 - seq2))) is V33() real ext-real Element of REAL
[((X - seq1) + (seq2 - seq2)),((X - seq1) + (seq2 - seq2))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq1) + (seq2 - seq2)),((X - seq1) + (seq2 - seq2))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq1) + (seq2 - seq2)),((X - seq1) + (seq2 - seq2))) is V33() real ext-real Element of REAL
seq1 - (seq2 - seq2) is right_complementable Element of the carrier of a
- (seq2 - seq2) is right_complementable Element of the carrier of a
seq1 + (- (seq2 - seq2)) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- (seq2 - seq2))) is right_complementable Element of the carrier of a
X - (seq1 - (seq2 - seq2)) is right_complementable Element of the carrier of a
- (seq1 - (seq2 - seq2)) is right_complementable Element of the carrier of a
X + (- (seq1 - (seq2 - seq2))) is right_complementable Element of the carrier of a
the addF of a . (X,(- (seq1 - (seq2 - seq2)))) is right_complementable Element of the carrier of a
(a,(X - (seq1 - (seq2 - seq2)))) is V33() real ext-real Element of REAL
(a,(X - (seq1 - (seq2 - seq2))),(X - (seq1 - (seq2 - seq2)))) is V33() real ext-real Element of REAL
[(X - (seq1 - (seq2 - seq2))),(X - (seq1 - (seq2 - seq2)))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - (seq1 - (seq2 - seq2))),(X - (seq1 - (seq2 - seq2)))] is V33() real ext-real Element of REAL
sqrt (a,(X - (seq1 - (seq2 - seq2))),(X - (seq1 - (seq2 - seq2)))) is V33() real ext-real Element of REAL
seq1 - seq2 is right_complementable Element of the carrier of a
seq1 + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- seq2)) is right_complementable Element of the carrier of a
seq2 + (seq1 - seq2) is right_complementable Element of the carrier of a
the addF of a . (seq2,(seq1 - seq2)) is right_complementable Element of the carrier of a
X - (seq2 + (seq1 - seq2)) is right_complementable Element of the carrier of a
- (seq2 + (seq1 - seq2)) is right_complementable Element of the carrier of a
X + (- (seq2 + (seq1 - seq2))) is right_complementable Element of the carrier of a
the addF of a . (X,(- (seq2 + (seq1 - seq2)))) is right_complementable Element of the carrier of a
(a,(X - (seq2 + (seq1 - seq2)))) is V33() real ext-real Element of REAL
(a,(X - (seq2 + (seq1 - seq2))),(X - (seq2 + (seq1 - seq2)))) is V33() real ext-real Element of REAL
[(X - (seq2 + (seq1 - seq2))),(X - (seq2 + (seq1 - seq2)))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - (seq2 + (seq1 - seq2))),(X - (seq2 + (seq1 - seq2)))] is V33() real ext-real Element of REAL
sqrt (a,(X - (seq2 + (seq1 - seq2))),(X - (seq2 + (seq1 - seq2)))) is V33() real ext-real Element of REAL
(X - seq2) - (seq1 - seq2) is right_complementable Element of the carrier of a
- (seq1 - seq2) is right_complementable Element of the carrier of a
(X - seq2) + (- (seq1 - seq2)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- (seq1 - seq2))) is right_complementable Element of the carrier of a
(a,((X - seq2) - (seq1 - seq2))) is V33() real ext-real Element of REAL
(a,((X - seq2) - (seq1 - seq2)),((X - seq2) - (seq1 - seq2))) is V33() real ext-real Element of REAL
[((X - seq2) - (seq1 - seq2)),((X - seq2) - (seq1 - seq2))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) - (seq1 - seq2)),((X - seq2) - (seq1 - seq2))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) - (seq1 - seq2)),((X - seq2) - (seq1 - seq2))) is V33() real ext-real Element of REAL
(X - seq2) + (seq2 - seq1) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(seq2 - seq1)) is right_complementable Element of the carrier of a
(a,((X - seq2) + (seq2 - seq1))) is V33() real ext-real Element of REAL
(a,((X - seq2) + (seq2 - seq1)),((X - seq2) + (seq2 - seq1))) is V33() real ext-real Element of REAL
[((X - seq2) + (seq2 - seq1)),((X - seq2) + (seq2 - seq1))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) + (seq2 - seq1)),((X - seq2) + (seq2 - seq1))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) + (seq2 - seq1)),((X - seq2) + (seq2 - seq1))) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
(a,X,seq1) is V33() real ext-real Element of REAL
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1)) is V33() real ext-real Element of REAL
(a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq1),(X - seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq1),(X - seq1)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq1),(X - seq1)) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X + seq1 is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,seq1) is right_complementable Element of the carrier of a
seq2 is right_complementable Element of the carrier of a
(a,X,seq2) is V33() real ext-real Element of REAL
X - seq2 is right_complementable Element of the carrier of a
- seq2 is right_complementable Element of the carrier of a
X + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (X,(- seq2)) is right_complementable Element of the carrier of a
(a,(X - seq2)) is V33() real ext-real Element of REAL
(a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq2),(X - seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq2),(X - seq2)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
n is right_complementable Element of the carrier of a
seq2 + n is right_complementable Element of the carrier of a
the addF of a . (seq2,n) is right_complementable Element of the carrier of a
(a,(X + seq1),(seq2 + n)) is V33() real ext-real Element of REAL
(X + seq1) - (seq2 + n) is right_complementable Element of the carrier of a
- (seq2 + n) is right_complementable Element of the carrier of a
(X + seq1) + (- (seq2 + n)) is right_complementable Element of the carrier of a
the addF of a . ((X + seq1),(- (seq2 + n))) is right_complementable Element of the carrier of a
(a,((X + seq1) - (seq2 + n))) is V33() real ext-real Element of REAL
(a,((X + seq1) - (seq2 + n)),((X + seq1) - (seq2 + n))) is V33() real ext-real Element of REAL
[((X + seq1) - (seq2 + n)),((X + seq1) - (seq2 + n))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X + seq1) - (seq2 + n)),((X + seq1) - (seq2 + n))] is V33() real ext-real Element of REAL
sqrt (a,((X + seq1) - (seq2 + n)),((X + seq1) - (seq2 + n))) is V33() real ext-real Element of REAL
(a,seq1,n) is V33() real ext-real Element of REAL
seq1 - n is right_complementable Element of the carrier of a
- n is right_complementable Element of the carrier of a
seq1 + (- n) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- n)) is right_complementable Element of the carrier of a
(a,(seq1 - n)) is V33() real ext-real Element of REAL
(a,(seq1 - n),(seq1 - n)) is V33() real ext-real Element of REAL
[(seq1 - n),(seq1 - n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(seq1 - n),(seq1 - n)] is V33() real ext-real Element of REAL
sqrt (a,(seq1 - n),(seq1 - n)) is V33() real ext-real Element of REAL
(a,X,seq2) + (a,seq1,n) is V33() real ext-real Element of REAL
(- seq2) + (- n) is right_complementable Element of the carrier of a
the addF of a . ((- seq2),(- n)) is right_complementable Element of the carrier of a
((- seq2) + (- n)) + (X + seq1) is right_complementable Element of the carrier of a
the addF of a . (((- seq2) + (- n)),(X + seq1)) is right_complementable Element of the carrier of a
(a,(((- seq2) + (- n)) + (X + seq1))) is V33() real ext-real Element of REAL
(a,(((- seq2) + (- n)) + (X + seq1)),(((- seq2) + (- n)) + (X + seq1))) is V33() real ext-real Element of REAL
[(((- seq2) + (- n)) + (X + seq1)),(((- seq2) + (- n)) + (X + seq1))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(((- seq2) + (- n)) + (X + seq1)),(((- seq2) + (- n)) + (X + seq1))] is V33() real ext-real Element of REAL
sqrt (a,(((- seq2) + (- n)) + (X + seq1)),(((- seq2) + (- n)) + (X + seq1))) is V33() real ext-real Element of REAL
X + ((- seq2) + (- n)) is right_complementable Element of the carrier of a
the addF of a . (X,((- seq2) + (- n))) is right_complementable Element of the carrier of a
(X + ((- seq2) + (- n))) + seq1 is right_complementable Element of the carrier of a
the addF of a . ((X + ((- seq2) + (- n))),seq1) is right_complementable Element of the carrier of a
(a,((X + ((- seq2) + (- n))) + seq1)) is V33() real ext-real Element of REAL
(a,((X + ((- seq2) + (- n))) + seq1),((X + ((- seq2) + (- n))) + seq1)) is V33() real ext-real Element of REAL
[((X + ((- seq2) + (- n))) + seq1),((X + ((- seq2) + (- n))) + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X + ((- seq2) + (- n))) + seq1),((X + ((- seq2) + (- n))) + seq1)] is V33() real ext-real Element of REAL
sqrt (a,((X + ((- seq2) + (- n))) + seq1),((X + ((- seq2) + (- n))) + seq1)) is V33() real ext-real Element of REAL
(X - seq2) + (- n) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- n)) is right_complementable Element of the carrier of a
((X - seq2) + (- n)) + seq1 is right_complementable Element of the carrier of a
the addF of a . (((X - seq2) + (- n)),seq1) is right_complementable Element of the carrier of a
(a,(((X - seq2) + (- n)) + seq1)) is V33() real ext-real Element of REAL
(a,(((X - seq2) + (- n)) + seq1),(((X - seq2) + (- n)) + seq1)) is V33() real ext-real Element of REAL
[(((X - seq2) + (- n)) + seq1),(((X - seq2) + (- n)) + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(((X - seq2) + (- n)) + seq1),(((X - seq2) + (- n)) + seq1)] is V33() real ext-real Element of REAL
sqrt (a,(((X - seq2) + (- n)) + seq1),(((X - seq2) + (- n)) + seq1)) is V33() real ext-real Element of REAL
(X - seq2) + (seq1 - n) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(seq1 - n)) is right_complementable Element of the carrier of a
(a,((X - seq2) + (seq1 - n))) is V33() real ext-real Element of REAL
(a,((X - seq2) + (seq1 - n)),((X - seq2) + (seq1 - n))) is V33() real ext-real Element of REAL
[((X - seq2) + (seq1 - n)),((X - seq2) + (seq1 - n))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) + (seq1 - n)),((X - seq2) + (seq1 - n))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) + (seq1 - n)),((X - seq2) + (seq1 - n))) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
seq2 is right_complementable Element of the carrier of a
(a,X,seq2) is V33() real ext-real Element of REAL
X - seq2 is right_complementable Element of the carrier of a
- seq2 is right_complementable Element of the carrier of a
X + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (X,(- seq2)) is right_complementable Element of the carrier of a
(a,(X - seq2)) is V33() real ext-real Element of REAL
(a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(X - seq2),(X - seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq2),(X - seq2)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
n is right_complementable Element of the carrier of a
seq2 - n is right_complementable Element of the carrier of a
- n is right_complementable Element of the carrier of a
seq2 + (- n) is right_complementable Element of the carrier of a
the addF of a . (seq2,(- n)) is right_complementable Element of the carrier of a
(a,(X - seq1),(seq2 - n)) is V33() real ext-real Element of REAL
(X - seq1) - (seq2 - n) is right_complementable Element of the carrier of a
- (seq2 - n) is right_complementable Element of the carrier of a
(X - seq1) + (- (seq2 - n)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(- (seq2 - n))) is right_complementable Element of the carrier of a
(a,((X - seq1) - (seq2 - n))) is V33() real ext-real Element of REAL
(a,((X - seq1) - (seq2 - n)),((X - seq1) - (seq2 - n))) is V33() real ext-real Element of REAL
[((X - seq1) - (seq2 - n)),((X - seq1) - (seq2 - n))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq1) - (seq2 - n)),((X - seq1) - (seq2 - n))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq1) - (seq2 - n)),((X - seq1) - (seq2 - n))) is V33() real ext-real Element of REAL
(a,seq1,n) is V33() real ext-real Element of REAL
seq1 - n is right_complementable Element of the carrier of a
seq1 + (- n) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- n)) is right_complementable Element of the carrier of a
(a,(seq1 - n)) is V33() real ext-real Element of REAL
(a,(seq1 - n),(seq1 - n)) is V33() real ext-real Element of REAL
[(seq1 - n),(seq1 - n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(seq1 - n),(seq1 - n)] is V33() real ext-real Element of REAL
sqrt (a,(seq1 - n),(seq1 - n)) is V33() real ext-real Element of REAL
(a,X,seq2) + (a,seq1,n) is V33() real ext-real Element of REAL
(X - seq1) - seq2 is right_complementable Element of the carrier of a
(X - seq1) + (- seq2) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(- seq2)) is right_complementable Element of the carrier of a
((X - seq1) - seq2) + n is right_complementable Element of the carrier of a
the addF of a . (((X - seq1) - seq2),n) is right_complementable Element of the carrier of a
(a,(((X - seq1) - seq2) + n)) is V33() real ext-real Element of REAL
(a,(((X - seq1) - seq2) + n),(((X - seq1) - seq2) + n)) is V33() real ext-real Element of REAL
[(((X - seq1) - seq2) + n),(((X - seq1) - seq2) + n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(((X - seq1) - seq2) + n),(((X - seq1) - seq2) + n)] is V33() real ext-real Element of REAL
sqrt (a,(((X - seq1) - seq2) + n),(((X - seq1) - seq2) + n)) is V33() real ext-real Element of REAL
seq2 + seq1 is right_complementable Element of the carrier of a
the addF of a . (seq2,seq1) is right_complementable Element of the carrier of a
X - (seq2 + seq1) is right_complementable Element of the carrier of a
- (seq2 + seq1) is right_complementable Element of the carrier of a
X + (- (seq2 + seq1)) is right_complementable Element of the carrier of a
the addF of a . (X,(- (seq2 + seq1))) is right_complementable Element of the carrier of a
(X - (seq2 + seq1)) + n is right_complementable Element of the carrier of a
the addF of a . ((X - (seq2 + seq1)),n) is right_complementable Element of the carrier of a
(a,((X - (seq2 + seq1)) + n)) is V33() real ext-real Element of REAL
(a,((X - (seq2 + seq1)) + n),((X - (seq2 + seq1)) + n)) is V33() real ext-real Element of REAL
[((X - (seq2 + seq1)) + n),((X - (seq2 + seq1)) + n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - (seq2 + seq1)) + n),((X - (seq2 + seq1)) + n)] is V33() real ext-real Element of REAL
sqrt (a,((X - (seq2 + seq1)) + n),((X - (seq2 + seq1)) + n)) is V33() real ext-real Element of REAL
(X - seq2) - seq1 is right_complementable Element of the carrier of a
(X - seq2) + (- seq1) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- seq1)) is right_complementable Element of the carrier of a
((X - seq2) - seq1) + n is right_complementable Element of the carrier of a
the addF of a . (((X - seq2) - seq1),n) is right_complementable Element of the carrier of a
(a,(((X - seq2) - seq1) + n)) is V33() real ext-real Element of REAL
(a,(((X - seq2) - seq1) + n),(((X - seq2) - seq1) + n)) is V33() real ext-real Element of REAL
[(((X - seq2) - seq1) + n),(((X - seq2) - seq1) + n)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(((X - seq2) - seq1) + n),(((X - seq2) - seq1) + n)] is V33() real ext-real Element of REAL
sqrt (a,(((X - seq2) - seq1) + n),(((X - seq2) - seq1) + n)) is V33() real ext-real Element of REAL
(X - seq2) - (seq1 - n) is right_complementable Element of the carrier of a
- (seq1 - n) is right_complementable Element of the carrier of a
(X - seq2) + (- (seq1 - n)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- (seq1 - n))) is right_complementable Element of the carrier of a
(a,((X - seq2) - (seq1 - n))) is V33() real ext-real Element of REAL
(a,((X - seq2) - (seq1 - n)),((X - seq2) - (seq1 - n))) is V33() real ext-real Element of REAL
[((X - seq2) - (seq1 - n)),((X - seq2) - (seq1 - n))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) - (seq1 - n)),((X - seq2) - (seq1 - n))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) - (seq1 - n)),((X - seq2) - (seq1 - n))) is V33() real ext-real Element of REAL
(X - seq2) + (- (seq1 - n)) is right_complementable Element of the carrier of a
(a,((X - seq2) + (- (seq1 - n)))) is V33() real ext-real Element of REAL
(a,((X - seq2) + (- (seq1 - n))),((X - seq2) + (- (seq1 - n)))) is V33() real ext-real Element of REAL
[((X - seq2) + (- (seq1 - n))),((X - seq2) + (- (seq1 - n)))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) + (- (seq1 - n))),((X - seq2) + (- (seq1 - n)))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) + (- (seq1 - n))),((X - seq2) + (- (seq1 - n)))) is V33() real ext-real Element of REAL
(a,(- (seq1 - n))) is V33() real ext-real Element of REAL
(a,(- (seq1 - n)),(- (seq1 - n))) is V33() real ext-real Element of REAL
[(- (seq1 - n)),(- (seq1 - n))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- (seq1 - n)),(- (seq1 - n))] is V33() real ext-real Element of REAL
sqrt (a,(- (seq1 - n)),(- (seq1 - n))) is V33() real ext-real Element of REAL
(a,(X - seq2)) + (a,(- (seq1 - n))) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
seq2 is right_complementable Element of the carrier of a
seq2 - seq1 is right_complementable Element of the carrier of a
seq2 + (- seq1) is right_complementable Element of the carrier of a
the addF of a . (seq2,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1),(seq2 - seq1)) is V33() real ext-real Element of REAL
(X - seq1) - (seq2 - seq1) is right_complementable Element of the carrier of a
- (seq2 - seq1) is right_complementable Element of the carrier of a
(X - seq1) + (- (seq2 - seq1)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(- (seq2 - seq1))) is right_complementable Element of the carrier of a
(a,((X - seq1) - (seq2 - seq1))) is V33() real ext-real Element of REAL
(a,((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))) is V33() real ext-real Element of REAL
(a,X,seq2) is V33() real ext-real Element of REAL
X - seq2 is right_complementable Element of the carrier of a
- seq2 is right_complementable Element of the carrier of a
X + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (X,(- seq2)) is right_complementable Element of the carrier of a
(a,(X - seq2)) is V33() real ext-real Element of REAL
(a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
[(X - seq2),(X - seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(X - seq2),(X - seq2)] is V33() real ext-real Element of REAL
sqrt (a,(X - seq2),(X - seq2)) is V33() real ext-real Element of REAL
(X - seq1) - seq2 is right_complementable Element of the carrier of a
(X - seq1) + (- seq2) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(- seq2)) is right_complementable Element of the carrier of a
((X - seq1) - seq2) + seq1 is right_complementable Element of the carrier of a
the addF of a . (((X - seq1) - seq2),seq1) is right_complementable Element of the carrier of a
(a,(((X - seq1) - seq2) + seq1)) is V33() real ext-real Element of REAL
(a,(((X - seq1) - seq2) + seq1),(((X - seq1) - seq2) + seq1)) is V33() real ext-real Element of REAL
[(((X - seq1) - seq2) + seq1),(((X - seq1) - seq2) + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(((X - seq1) - seq2) + seq1),(((X - seq1) - seq2) + seq1)] is V33() real ext-real Element of REAL
sqrt (a,(((X - seq1) - seq2) + seq1),(((X - seq1) - seq2) + seq1)) is V33() real ext-real Element of REAL
seq2 + seq1 is right_complementable Element of the carrier of a
the addF of a . (seq2,seq1) is right_complementable Element of the carrier of a
X - (seq2 + seq1) is right_complementable Element of the carrier of a
- (seq2 + seq1) is right_complementable Element of the carrier of a
X + (- (seq2 + seq1)) is right_complementable Element of the carrier of a
the addF of a . (X,(- (seq2 + seq1))) is right_complementable Element of the carrier of a
(X - (seq2 + seq1)) + seq1 is right_complementable Element of the carrier of a
the addF of a . ((X - (seq2 + seq1)),seq1) is right_complementable Element of the carrier of a
(a,((X - (seq2 + seq1)) + seq1)) is V33() real ext-real Element of REAL
(a,((X - (seq2 + seq1)) + seq1),((X - (seq2 + seq1)) + seq1)) is V33() real ext-real Element of REAL
[((X - (seq2 + seq1)) + seq1),((X - (seq2 + seq1)) + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - (seq2 + seq1)) + seq1),((X - (seq2 + seq1)) + seq1)] is V33() real ext-real Element of REAL
sqrt (a,((X - (seq2 + seq1)) + seq1),((X - (seq2 + seq1)) + seq1)) is V33() real ext-real Element of REAL
(X - seq2) - seq1 is right_complementable Element of the carrier of a
(X - seq2) + (- seq1) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- seq1)) is right_complementable Element of the carrier of a
((X - seq2) - seq1) + seq1 is right_complementable Element of the carrier of a
the addF of a . (((X - seq2) - seq1),seq1) is right_complementable Element of the carrier of a
(a,(((X - seq2) - seq1) + seq1)) is V33() real ext-real Element of REAL
(a,(((X - seq2) - seq1) + seq1),(((X - seq2) - seq1) + seq1)) is V33() real ext-real Element of REAL
[(((X - seq2) - seq1) + seq1),(((X - seq2) - seq1) + seq1)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(((X - seq2) - seq1) + seq1),(((X - seq2) - seq1) + seq1)] is V33() real ext-real Element of REAL
sqrt (a,(((X - seq2) - seq1) + seq1),(((X - seq2) - seq1) + seq1)) is V33() real ext-real Element of REAL
seq1 - seq1 is right_complementable Element of the carrier of a
seq1 + (- seq1) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- seq1)) is right_complementable Element of the carrier of a
(X - seq2) - (seq1 - seq1) is right_complementable Element of the carrier of a
- (seq1 - seq1) is right_complementable Element of the carrier of a
(X - seq2) + (- (seq1 - seq1)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- (seq1 - seq1))) is right_complementable Element of the carrier of a
(a,((X - seq2) - (seq1 - seq1))) is V33() real ext-real Element of REAL
(a,((X - seq2) - (seq1 - seq1)),((X - seq2) - (seq1 - seq1))) is V33() real ext-real Element of REAL
[((X - seq2) - (seq1 - seq1)),((X - seq2) - (seq1 - seq1))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) - (seq1 - seq1)),((X - seq2) - (seq1 - seq1))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) - (seq1 - seq1)),((X - seq2) - (seq1 - seq1))) is V33() real ext-real Element of REAL
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
(X - seq2) - H1(a) is right_complementable Element of the carrier of a
- (0. a) is right_complementable Element of the carrier of a
(X - seq2) + (- (0. a)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq2),(- (0. a))) is right_complementable Element of the carrier of a
(a,((X - seq2) - H1(a))) is V33() real ext-real Element of REAL
(a,((X - seq2) - H1(a)),((X - seq2) - H1(a))) is V33() real ext-real Element of REAL
[((X - seq2) - H1(a)),((X - seq2) - H1(a))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq2) - H1(a)),((X - seq2) - H1(a))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq2) - H1(a)),((X - seq2) - H1(a))) is V33() real ext-real Element of REAL
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
X is right_complementable Element of the carrier of a
seq1 is right_complementable Element of the carrier of a
X - seq1 is right_complementable Element of the carrier of a
- seq1 is right_complementable Element of the carrier of a
X + (- seq1) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (X,(- seq1)) is right_complementable Element of the carrier of a
(a,seq1,X) is V33() real ext-real Element of REAL
seq1 - X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 + (- X) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- X)) is right_complementable Element of the carrier of a
(a,(seq1 - X)) is V33() real ext-real Element of REAL
(a,(seq1 - X),(seq1 - X)) is V33() real ext-real Element of REAL
the of a is Relation-like [: the carrier of a, the carrier of a:] -defined REAL -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], REAL ) Element of bool [:[: the carrier of a, the carrier of a:],REAL:]
[:[: the carrier of a, the carrier of a:],REAL:] is non empty set
bool [:[: the carrier of a, the carrier of a:],REAL:] is non empty set
[(seq1 - X),(seq1 - X)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(seq1 - X),(seq1 - X)] is V33() real ext-real Element of REAL
sqrt (a,(seq1 - X),(seq1 - X)) is V33() real ext-real Element of REAL
seq2 is right_complementable Element of the carrier of a
seq2 - seq1 is right_complementable Element of the carrier of a
seq2 + (- seq1) is right_complementable Element of the carrier of a
the addF of a . (seq2,(- seq1)) is right_complementable Element of the carrier of a
(a,(X - seq1),(seq2 - seq1)) is V33() real ext-real Element of REAL
(X - seq1) - (seq2 - seq1) is right_complementable Element of the carrier of a
- (seq2 - seq1) is right_complementable Element of the carrier of a
(X - seq1) + (- (seq2 - seq1)) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(- (seq2 - seq1))) is right_complementable Element of the carrier of a
(a,((X - seq1) - (seq2 - seq1))) is V33() real ext-real Element of REAL
(a,((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))) is V33() real ext-real Element of REAL
[((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq1) - (seq2 - seq1)),((X - seq1) - (seq2 - seq1))) is V33() real ext-real Element of REAL
(a,seq1,seq2) is V33() real ext-real Element of REAL
seq1 - seq2 is right_complementable Element of the carrier of a
- seq2 is right_complementable Element of the carrier of a
seq1 + (- seq2) is right_complementable Element of the carrier of a
the addF of a . (seq1,(- seq2)) is right_complementable Element of the carrier of a
(a,(seq1 - seq2)) is V33() real ext-real Element of REAL
(a,(seq1 - seq2),(seq1 - seq2)) is V33() real ext-real Element of REAL
[(seq1 - seq2),(seq1 - seq2)] is Element of [: the carrier of a, the carrier of a:]
the of a . [(seq1 - seq2),(seq1 - seq2)] is V33() real ext-real Element of REAL
sqrt (a,(seq1 - seq2),(seq1 - seq2)) is V33() real ext-real Element of REAL
(a,seq1,X) + (a,seq1,seq2) is V33() real ext-real Element of REAL
(X - seq1) + (seq1 - seq2) is right_complementable Element of the carrier of a
the addF of a . ((X - seq1),(seq1 - seq2)) is right_complementable Element of the carrier of a
(a,((X - seq1) + (seq1 - seq2))) is V33() real ext-real Element of REAL
(a,((X - seq1) + (seq1 - seq2)),((X - seq1) + (seq1 - seq2))) is V33() real ext-real Element of REAL
[((X - seq1) + (seq1 - seq2)),((X - seq1) + (seq1 - seq2))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((X - seq1) + (seq1 - seq2)),((X - seq1) + (seq1 - seq2))] is V33() real ext-real Element of REAL
sqrt (a,((X - seq1) + (seq1 - seq2)),((X - seq1) + (seq1 - seq2))) is V33() real ext-real Element of REAL
- (seq1 - X) is right_complementable Element of the carrier of a
(- (seq1 - X)) + (seq1 - seq2) is right_complementable Element of the carrier of a
the addF of a . ((- (seq1 - X)),(seq1 - seq2)) is right_complementable Element of the carrier of a
(a,((- (seq1 - X)) + (seq1 - seq2))) is V33() real ext-real Element of REAL
(a,((- (seq1 - X)) + (seq1 - seq2)),((- (seq1 - X)) + (seq1 - seq2))) is V33() real ext-real Element of REAL
[((- (seq1 - X)) + (seq1 - seq2)),((- (seq1 - X)) + (seq1 - seq2))] is Element of [: the carrier of a, the carrier of a:]
the of a . [((- (seq1 - X)) + (seq1 - seq2)),((- (seq1 - X)) + (seq1 - seq2))] is V33() real ext-real Element of REAL
sqrt (a,((- (seq1 - X)) + (seq1 - seq2)),((- (seq1 - X)) + (seq1 - seq2))) is V33() real ext-real Element of REAL
(a,(- (seq1 - X))) is V33() real ext-real Element of REAL
(a,(- (seq1 - X)),(- (seq1 - X))) is V33() real ext-real Element of REAL
[(- (seq1 - X)),(- (seq1 - X))] is Element of [: the carrier of a, the carrier of a:]
the of a . [(- (seq1 - X)),(- (seq1 - X))] is V33() real ext-real Element of REAL
sqrt (a,(- (seq1 - X)),(- (seq1 - X))) is V33() real ext-real Element of REAL
(a,(- (seq1 - X))) + (a,(seq1 - seq2)) is V33() real ext-real Element of REAL
a is non empty addLoopStr
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Element of the carrier of a
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
z is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
seq2 . z is set
n . z is set
seq2 . z is Element of the carrier of a
X . z is Element of the carrier of a
(X . z) + seq1 is Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . z),seq1) is Element of the carrier of a
a is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
X is non empty addLoopStr
the carrier of X is non empty set
[:NAT, the carrier of X:] is non empty set
bool [:NAT, the carrier of X:] is non empty set
seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
- seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
(- seq1) . a is Element of the carrier of X
seq1 . a is Element of the carrier of X
- (seq1 . a) is Element of the carrier of X
dom (- seq1) is set
(- seq1) /. a is Element of the carrier of X
(- seq1) . a is Element of the carrier of X
seq1 /. a is Element of the carrier of X
seq1 . a is Element of the carrier of X
- (seq1 /. a) is Element of the carrier of X
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 + n is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n + seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
z is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(seq2 + n) . z is set
(n + seq2) . z is set
(seq2 + n) . z is right_complementable Element of the carrier of a
n . z is right_complementable Element of the carrier of a
seq2 . z is right_complementable Element of the carrier of a
(n . z) + (seq2 . z) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((n . z),(seq2 . z)) is right_complementable Element of the carrier of a
(n + seq2) . z is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,seq1) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,seq1,seq2) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,(a,seq1,seq2)) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,(a,X,seq1),seq2) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(a,X,(a,seq1,seq2)) . n is set
(a,(a,X,seq1),seq2) . n is set
(a,X,(a,seq1,seq2)) . n is right_complementable Element of the carrier of a
X . n is right_complementable Element of the carrier of a
(a,seq1,seq2) . n is right_complementable Element of the carrier of a
(X . n) + ((a,seq1,seq2) . n) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . n),((a,seq1,seq2) . n)) is right_complementable Element of the carrier of a
seq1 . n is right_complementable Element of the carrier of a
seq2 . n is right_complementable Element of the carrier of a
(seq1 . n) + (seq2 . n) is right_complementable Element of the carrier of a
the addF of a . ((seq1 . n),(seq2 . n)) is right_complementable Element of the carrier of a
(X . n) + ((seq1 . n) + (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . ((X . n),((seq1 . n) + (seq2 . n))) is right_complementable Element of the carrier of a
(X . n) + (seq1 . n) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(seq1 . n)) is right_complementable Element of the carrier of a
((X . n) + (seq1 . n)) + (seq2 . n) is right_complementable Element of the carrier of a
the addF of a . (((X . n) + (seq1 . n)),(seq2 . n)) is right_complementable Element of the carrier of a
(a,X,seq1) . n is right_complementable Element of the carrier of a
((a,X,seq1) . n) + (seq2 . n) is right_complementable Element of the carrier of a
the addF of a . (((a,X,seq1) . n),(seq2 . n)) is right_complementable Element of the carrier of a
(a,(a,X,seq1),seq2) . n is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,seq1) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is right_complementable Element of the carrier of a
z is right_complementable Element of the carrier of a
n + z is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (n,z) is right_complementable Element of the carrier of a
n is right_complementable Element of the carrier of a
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real set
(a,X,seq1) . n is set
(a,X,seq1) . n is right_complementable Element of the carrier of a
X . n is right_complementable Element of the carrier of a
seq1 . n is right_complementable Element of the carrier of a
(X . n) + (seq1 . n) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(seq1 . n)) is right_complementable Element of the carrier of a
n + (seq1 . n) is right_complementable Element of the carrier of a
the addF of a . (n,(seq1 . n)) is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is right_complementable Element of the carrier of a
z is right_complementable Element of the carrier of a
n - z is right_complementable Element of the carrier of a
- z is right_complementable Element of the carrier of a
n + (- z) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (n,(- z)) is right_complementable Element of the carrier of a
n is right_complementable Element of the carrier of a
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real set
(X - seq1) . n is set
(X - seq1) . n is right_complementable Element of the carrier of a
X . n is right_complementable Element of the carrier of a
seq1 . n is right_complementable Element of the carrier of a
(X . n) - (seq1 . n) is right_complementable Element of the carrier of a
- (seq1 . n) is right_complementable Element of the carrier of a
(X . n) + (- (seq1 . n)) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(- (seq1 . n))) is right_complementable Element of the carrier of a
n - (seq1 . n) is right_complementable Element of the carrier of a
n + (- (seq1 . n)) is right_complementable Element of the carrier of a
the addF of a . (n,(- (seq1 . n))) is right_complementable Element of the carrier of a
a is V33() real ext-real Element of REAL
X is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of X is non empty set
[:NAT, the carrier of X:] is non empty set
bool [:NAT, the carrier of X:] is non empty set
seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
n is right_complementable Element of the carrier of X
a * n is right_complementable Element of the carrier of X
the Mult of X is Relation-like [:REAL, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: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 non empty set
[:[:REAL, the carrier of X:], the carrier of X:] is non empty set
bool [:[:REAL, the carrier of X:], the carrier of X:] is non empty set
the Mult of X . (a,n) is set
z is right_complementable Element of the carrier of X
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real set
(a * seq1) . n is set
(a * seq1) . n is right_complementable Element of the carrier of X
seq1 . n is right_complementable Element of the carrier of X
a * (seq1 . n) is right_complementable Element of the carrier of X
the Mult of X . (a,(seq1 . n)) is set
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
- seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,(- seq1)) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(X - seq1) . seq2 is set
(a,X,(- seq1)) . seq2 is set
(X - seq1) . seq2 is right_complementable Element of the carrier of a
X . seq2 is right_complementable Element of the carrier of a
seq1 . seq2 is right_complementable Element of the carrier of a
(X . seq2) - (seq1 . seq2) is right_complementable Element of the carrier of a
- (seq1 . seq2) is right_complementable Element of the carrier of a
(X . seq2) + (- (seq1 . seq2)) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . seq2),(- (seq1 . seq2))) is right_complementable Element of the carrier of a
(- seq1) . seq2 is right_complementable Element of the carrier of a
(X . seq2) + ((- seq1) . seq2) is right_complementable Element of the carrier of a
the addF of a . ((X . seq2),((- seq1) . seq2)) is right_complementable Element of the carrier of a
(a,X,(- seq1)) . seq2 is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,(0. a)) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
X . seq1 is set
(a,X,(0. a)) . seq1 is set
(a,X,H1(a)) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,H1(a)) . seq1 is right_complementable Element of the carrier of a
X . seq1 is right_complementable Element of the carrier of a
(X . seq1) + H1(a) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . seq1),(0. a)) is right_complementable Element of the carrier of a
a is V33() real ext-real Element of REAL
X is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of X is non empty set
[:NAT, the carrier of X:] is non empty set
bool [:NAT, the carrier of X:] is non empty set
seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
seq2 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
(X,seq1,seq2) is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * (X,seq1,seq2) is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * seq2 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
(X,(a * seq1),(a * seq2)) is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(a * (X,seq1,seq2)) . n is set
(X,(a * seq1),(a * seq2)) . n is set
(a * (X,seq1,seq2)) . n is right_complementable Element of the carrier of X
(X,seq1,seq2) . n is right_complementable Element of the carrier of X
a * ((X,seq1,seq2) . n) is right_complementable Element of the carrier of X
the Mult of X is Relation-like [:REAL, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: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 non empty set
[:[:REAL, the carrier of X:], the carrier of X:] is non empty set
bool [:[:REAL, the carrier of X:], the carrier of X:] is non empty set
the Mult of X . (a,((X,seq1,seq2) . n)) is set
seq1 . n is right_complementable Element of the carrier of X
seq2 . n is right_complementable Element of the carrier of X
(seq1 . n) + (seq2 . n) is right_complementable Element of the carrier of X
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: 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 non empty set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of X . ((seq1 . n),(seq2 . n)) is right_complementable Element of the carrier of X
a * ((seq1 . n) + (seq2 . n)) is right_complementable Element of the carrier of X
the Mult of X . (a,((seq1 . n) + (seq2 . n))) is set
a * (seq1 . n) is right_complementable Element of the carrier of X
the Mult of X . (a,(seq1 . n)) is set
a * (seq2 . n) is right_complementable Element of the carrier of X
the Mult of X . (a,(seq2 . n)) is set
(a * (seq1 . n)) + (a * (seq2 . n)) is right_complementable Element of the carrier of X
the addF of X . ((a * (seq1 . n)),(a * (seq2 . n))) is right_complementable Element of the carrier of X
(a * seq1) . n is right_complementable Element of the carrier of X
((a * seq1) . n) + (a * (seq2 . n)) is right_complementable Element of the carrier of X
the addF of X . (((a * seq1) . n),(a * (seq2 . n))) is right_complementable Element of the carrier of X
(a * seq2) . n is right_complementable Element of the carrier of X
((a * seq1) . n) + ((a * seq2) . n) is right_complementable Element of the carrier of X
the addF of X . (((a * seq1) . n),((a * seq2) . n)) is right_complementable Element of the carrier of X
(X,(a * seq1),(a * seq2)) . n is right_complementable Element of the carrier of X
a is V33() real ext-real Element of REAL
X is V33() real ext-real Element of REAL
a + X is V33() real ext-real Element of REAL
seq1 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq1 is non empty set
[:NAT, the carrier of seq1:] is non empty set
bool [:NAT, the carrier of seq1:] is non empty set
seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
(a + X) * seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
a * seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
X * seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
(seq1,(a * seq2),(X * seq2)) is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
((a + X) * seq2) . n is set
(seq1,(a * seq2),(X * seq2)) . n is set
((a + X) * seq2) . n is right_complementable Element of the carrier of seq1
seq2 . n is right_complementable Element of the carrier of seq1
(a + X) * (seq2 . n) is right_complementable Element of the carrier of seq1
the Mult of seq1 is Relation-like [:REAL, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([:REAL, the carrier of seq1:], the carrier of seq1) Element of bool [:[:REAL, the carrier of seq1:], the carrier of seq1:]
[:REAL, the carrier of seq1:] is non empty set
[:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
the Mult of seq1 . ((a + X),(seq2 . n)) is set
a * (seq2 . n) is right_complementable Element of the carrier of seq1
the Mult of seq1 . (a,(seq2 . n)) is set
X * (seq2 . n) is right_complementable Element of the carrier of seq1
the Mult of seq1 . (X,(seq2 . n)) is set
(a * (seq2 . n)) + (X * (seq2 . n)) is right_complementable Element of the carrier of seq1
the addF of seq1 is Relation-like [: the carrier of seq1, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([: the carrier of seq1, the carrier of seq1:], the carrier of seq1) Element of bool [:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:]
[: the carrier of seq1, the carrier of seq1:] is non empty set
[:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[: the carrier of seq1, the carrier of seq1:], the carrier of seq1:] is non empty set
the addF of seq1 . ((a * (seq2 . n)),(X * (seq2 . n))) is right_complementable Element of the carrier of seq1
(a * seq2) . n is right_complementable Element of the carrier of seq1
((a * seq2) . n) + (X * (seq2 . n)) is right_complementable Element of the carrier of seq1
the addF of seq1 . (((a * seq2) . n),(X * (seq2 . n))) is right_complementable Element of the carrier of seq1
(X * seq2) . n is right_complementable Element of the carrier of seq1
((a * seq2) . n) + ((X * seq2) . n) is right_complementable Element of the carrier of seq1
the addF of seq1 . (((a * seq2) . n),((X * seq2) . n)) is right_complementable Element of the carrier of seq1
(seq1,(a * seq2),(X * seq2)) . n is right_complementable Element of the carrier of seq1
a is V33() real ext-real Element of REAL
X is V33() real ext-real Element of REAL
a * X is V33() real ext-real Element of REAL
seq1 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq1 is non empty set
[:NAT, the carrier of seq1:] is non empty set
bool [:NAT, the carrier of seq1:] is non empty set
seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
(a * X) * seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
X * seq2 is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
a * (X * seq2) is Relation-like NAT -defined the carrier of seq1 -valued Function-like non empty total V18( NAT , the carrier of seq1) Element of bool [:NAT, the carrier of seq1:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
((a * X) * seq2) . n is set
(a * (X * seq2)) . n is set
((a * X) * seq2) . n is right_complementable Element of the carrier of seq1
seq2 . n is right_complementable Element of the carrier of seq1
(a * X) * (seq2 . n) is right_complementable Element of the carrier of seq1
the Mult of seq1 is Relation-like [:REAL, the carrier of seq1:] -defined the carrier of seq1 -valued Function-like non empty total V18([:REAL, the carrier of seq1:], the carrier of seq1) Element of bool [:[:REAL, the carrier of seq1:], the carrier of seq1:]
[:REAL, the carrier of seq1:] is non empty set
[:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
bool [:[:REAL, the carrier of seq1:], the carrier of seq1:] is non empty set
the Mult of seq1 . ((a * X),(seq2 . n)) is set
X * (seq2 . n) is right_complementable Element of the carrier of seq1
the Mult of seq1 . (X,(seq2 . n)) is set
a * (X * (seq2 . n)) is right_complementable Element of the carrier of seq1
the Mult of seq1 . (a,(X * (seq2 . n))) is set
(X * seq2) . n is right_complementable Element of the carrier of seq1
a * ((X * seq2) . n) is right_complementable Element of the carrier of seq1
the Mult of seq1 . (a,((X * seq2) . n)) is set
(a * (X * seq2)) . n is right_complementable Element of the carrier of seq1
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
1 * X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(1 * X) . seq1 is set
X . seq1 is set
(1 * X) . seq1 is right_complementable Element of the carrier of a
X . seq1 is right_complementable Element of the carrier of a
1 * (X . seq1) is right_complementable Element of the carrier of a
the Mult of a is Relation-like [:REAL, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([:REAL, the carrier of a:], the carrier of a) Element of bool [:[:REAL, the carrier of a:], the carrier of a:]
[:REAL, the carrier of a:] is non empty set
[:[:REAL, the carrier of a:], the carrier of a:] is non empty set
bool [:[:REAL, the carrier of a:], the carrier of a:] is non empty set
the Mult of a . (1,(X . seq1)) is set
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(- 1) * X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
- X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
((- 1) * X) . seq1 is set
(- X) . seq1 is set
((- 1) * X) . seq1 is right_complementable Element of the carrier of a
X . seq1 is right_complementable Element of the carrier of a
(- 1) * (X . seq1) is right_complementable Element of the carrier of a
the Mult of a is Relation-like [:REAL, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([:REAL, the carrier of a:], the carrier of a) Element of bool [:[:REAL, the carrier of a:], the carrier of a:]
[:REAL, the carrier of a:] is non empty set
[:[:REAL, the carrier of a:], the carrier of a:] is non empty set
bool [:[:REAL, the carrier of a:], the carrier of a:] is non empty set
the Mult of a . ((- 1),(X . seq1)) is set
- (X . seq1) is right_complementable Element of the carrier of a
(- X) . seq1 is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is right_complementable Element of the carrier of a
- X is right_complementable Element of the carrier of a
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 - X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,seq1,(- X)) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(seq1 - X) . seq2 is set
(a,seq1,(- X)) . seq2 is set
(seq1 - X) . seq2 is right_complementable Element of the carrier of a
seq1 . seq2 is right_complementable Element of the carrier of a
(seq1 . seq2) - X is right_complementable Element of the carrier of a
(seq1 . seq2) + (- X) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((seq1 . seq2),(- X)) is right_complementable Element of the carrier of a
(a,seq1,(- X)) . seq2 is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 - X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
- (seq1 - X) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(X - seq1) . seq2 is set
(- (seq1 - X)) . seq2 is set
(X - seq1) . seq2 is right_complementable Element of the carrier of a
X . seq2 is right_complementable Element of the carrier of a
seq1 . seq2 is right_complementable Element of the carrier of a
(X . seq2) - (seq1 . seq2) is right_complementable Element of the carrier of a
- (seq1 . seq2) is right_complementable Element of the carrier of a
(X . seq2) + (- (seq1 . seq2)) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . seq2),(- (seq1 . seq2))) is right_complementable Element of the carrier of a
(seq1 . seq2) - (X . seq2) is right_complementable Element of the carrier of a
- (X . seq2) is right_complementable Element of the carrier of a
(seq1 . seq2) + (- (X . seq2)) is right_complementable Element of the carrier of a
the addF of a . ((seq1 . seq2),(- (X . seq2))) is right_complementable Element of the carrier of a
- ((seq1 . seq2) - (X . seq2)) is right_complementable Element of the carrier of a
(seq1 - X) . seq2 is right_complementable Element of the carrier of a
- ((seq1 - X) . seq2) is right_complementable Element of the carrier of a
(- (seq1 - X)) . seq2 is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
0. a is V74(a) right_complementable Element of the carrier of a
the ZeroF of a is right_complementable Element of the carrier of a
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - (0. a) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
X . seq1 is set
(X - (0. a)) . seq1 is set
X - H1(a) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(X - H1(a)) . seq1 is right_complementable Element of the carrier of a
X . seq1 is right_complementable Element of the carrier of a
(X . seq1) - H1(a) is right_complementable Element of the carrier of a
- (0. a) is right_complementable Element of the carrier of a
(X . seq1) + (- (0. a)) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . seq1),(- (0. a))) is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
- X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
- (- X) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
X . seq1 is set
(- (- X)) . seq1 is set
(- (- X)) . seq1 is right_complementable Element of the carrier of a
(- X) . seq1 is right_complementable Element of the carrier of a
- ((- X) . seq1) is right_complementable Element of the carrier of a
X . seq1 is right_complementable Element of the carrier of a
- (X . seq1) is right_complementable Element of the carrier of a
- (- (X . seq1)) is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,seq1,seq2) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - (a,seq1,seq2) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(X - seq1) - seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(X - (a,seq1,seq2)) . n is set
((X - seq1) - seq2) . n is set
(X - (a,seq1,seq2)) . n is right_complementable Element of the carrier of a
X . n is right_complementable Element of the carrier of a
(a,seq1,seq2) . n is right_complementable Element of the carrier of a
(X . n) - ((a,seq1,seq2) . n) is right_complementable Element of the carrier of a
- ((a,seq1,seq2) . n) is right_complementable Element of the carrier of a
(X . n) + (- ((a,seq1,seq2) . n)) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . n),(- ((a,seq1,seq2) . n))) is right_complementable Element of the carrier of a
seq1 . n is right_complementable Element of the carrier of a
seq2 . n is right_complementable Element of the carrier of a
(seq1 . n) + (seq2 . n) is right_complementable Element of the carrier of a
the addF of a . ((seq1 . n),(seq2 . n)) is right_complementable Element of the carrier of a
(X . n) - ((seq1 . n) + (seq2 . n)) is right_complementable Element of the carrier of a
- ((seq1 . n) + (seq2 . n)) is right_complementable Element of the carrier of a
(X . n) + (- ((seq1 . n) + (seq2 . n))) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(- ((seq1 . n) + (seq2 . n)))) is right_complementable Element of the carrier of a
(X . n) - (seq1 . n) is right_complementable Element of the carrier of a
- (seq1 . n) is right_complementable Element of the carrier of a
(X . n) + (- (seq1 . n)) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(- (seq1 . n))) is right_complementable Element of the carrier of a
((X . n) - (seq1 . n)) - (seq2 . n) is right_complementable Element of the carrier of a
- (seq2 . n) is right_complementable Element of the carrier of a
((X . n) - (seq1 . n)) + (- (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . (((X . n) - (seq1 . n)),(- (seq2 . n))) is right_complementable Element of the carrier of a
(X - seq1) . n is right_complementable Element of the carrier of a
((X - seq1) . n) - (seq2 . n) is right_complementable Element of the carrier of a
((X - seq1) . n) + (- (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . (((X - seq1) . n),(- (seq2 . n))) is right_complementable Element of the carrier of a
((X - seq1) - seq2) . n is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,seq1) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,seq1) - seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 - seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,X,(seq1 - seq2)) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
((a,X,seq1) - seq2) . n is set
(a,X,(seq1 - seq2)) . n is set
((a,X,seq1) - seq2) . n is right_complementable Element of the carrier of a
(a,X,seq1) . n is right_complementable Element of the carrier of a
seq2 . n is right_complementable Element of the carrier of a
((a,X,seq1) . n) - (seq2 . n) is right_complementable Element of the carrier of a
- (seq2 . n) is right_complementable Element of the carrier of a
((a,X,seq1) . n) + (- (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (((a,X,seq1) . n),(- (seq2 . n))) is right_complementable Element of the carrier of a
X . n is right_complementable Element of the carrier of a
seq1 . n is right_complementable Element of the carrier of a
(X . n) + (seq1 . n) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(seq1 . n)) is right_complementable Element of the carrier of a
((X . n) + (seq1 . n)) - (seq2 . n) is right_complementable Element of the carrier of a
((X . n) + (seq1 . n)) + (- (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . (((X . n) + (seq1 . n)),(- (seq2 . n))) is right_complementable Element of the carrier of a
(seq1 . n) - (seq2 . n) is right_complementable Element of the carrier of a
(seq1 . n) + (- (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . ((seq1 . n),(- (seq2 . n))) is right_complementable Element of the carrier of a
(X . n) + ((seq1 . n) - (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . ((X . n),((seq1 . n) - (seq2 . n))) is right_complementable Element of the carrier of a
(seq1 - seq2) . n is right_complementable Element of the carrier of a
(X . n) + ((seq1 - seq2) . n) is right_complementable Element of the carrier of a
the addF of a . ((X . n),((seq1 - seq2) . n)) is right_complementable Element of the carrier of a
(a,X,(seq1 - seq2)) . n is right_complementable Element of the carrier of a
a is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of a is non empty set
[:NAT, the carrier of a:] is non empty set
bool [:NAT, the carrier of a:] is non empty set
X is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - seq1 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
seq1 - seq2 is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
X - (seq1 - seq2) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
(a,(X - seq1),seq2) is Relation-like NAT -defined the carrier of a -valued Function-like non empty total V18( NAT , the carrier of a) Element of bool [:NAT, the carrier of a:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(X - (seq1 - seq2)) . n is set
(a,(X - seq1),seq2) . n is set
(X - (seq1 - seq2)) . n is right_complementable Element of the carrier of a
X . n is right_complementable Element of the carrier of a
(seq1 - seq2) . n is right_complementable Element of the carrier of a
(X . n) - ((seq1 - seq2) . n) is right_complementable Element of the carrier of a
- ((seq1 - seq2) . n) is right_complementable Element of the carrier of a
(X . n) + (- ((seq1 - seq2) . n)) is right_complementable Element of the carrier of a
the addF of a is Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like non empty total V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((X . n),(- ((seq1 - seq2) . n))) is right_complementable Element of the carrier of a
seq1 . n is right_complementable Element of the carrier of a
seq2 . n is right_complementable Element of the carrier of a
(seq1 . n) - (seq2 . n) is right_complementable Element of the carrier of a
- (seq2 . n) is right_complementable Element of the carrier of a
(seq1 . n) + (- (seq2 . n)) is right_complementable Element of the carrier of a
the addF of a . ((seq1 . n),(- (seq2 . n))) is right_complementable Element of the carrier of a
(X . n) - ((seq1 . n) - (seq2 . n)) is right_complementable Element of the carrier of a
- ((seq1 . n) - (seq2 . n)) is right_complementable Element of the carrier of a
(X . n) + (- ((seq1 . n) - (seq2 . n))) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(- ((seq1 . n) - (seq2 . n)))) is right_complementable Element of the carrier of a
(X . n) - (seq1 . n) is right_complementable Element of the carrier of a
- (seq1 . n) is right_complementable Element of the carrier of a
(X . n) + (- (seq1 . n)) is right_complementable Element of the carrier of a
the addF of a . ((X . n),(- (seq1 . n))) is right_complementable Element of the carrier of a
((X . n) - (seq1 . n)) + (seq2 . n) is right_complementable Element of the carrier of a
the addF of a . (((X . n) - (seq1 . n)),(seq2 . n)) is right_complementable Element of the carrier of a
(X - seq1) . n is right_complementable Element of the carrier of a
((X - seq1) . n) + (seq2 . n) is right_complementable Element of the carrier of a
the addF of a . (((X - seq1) . n),(seq2 . n)) is right_complementable Element of the carrier of a
(a,(X - seq1),seq2) . n is right_complementable Element of the carrier of a
a is V33() real ext-real Element of REAL
X is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of X is non empty set
[:NAT, the carrier of X:] is non empty set
bool [:NAT, the carrier of X:] is non empty set
seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * seq1 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
seq2 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
seq1 - seq2 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * (seq1 - seq2) is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
a * seq2 is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
(a * seq1) - (a * seq2) is Relation-like NAT -defined the carrier of X -valued Function-like non empty total V18( NAT , the carrier of X) Element of bool [:NAT, the carrier of X:]
n is epsilon-transitive epsilon-connected ordinal natural V33() real ext-real V38() V39() V40() V41() V42() V43() Element of NAT
(a * (seq1 - seq2)) . n is set
((a * seq1) - (a * seq2)) . n is set
(a * (seq1 - seq2)) . n is right_complementable Element of the carrier of X
(seq1 - seq2) . n is right_complementable Element of the carrier of X
a * ((seq1 - seq2) . n) is right_complementable Element of the carrier of X
the Mult of X is Relation-like [:REAL, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: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 non empty set
[:[:REAL, the carrier of X:], the carrier of X:] is non empty set
bool [:[:REAL, the carrier of X:], the carrier of X:] is non empty set
the Mult of X . (a,((seq1 - seq2) . n)) is set
seq1 . n is right_complementable Element of the carrier of X
seq2 . n is right_complementable Element of the carrier of X
(seq1 . n) - (seq2 . n) is right_complementable Element of the carrier of X
- (seq2 . n) is right_complementable Element of the carrier of X
(seq1 . n) + (- (seq2 . n)) is right_complementable Element of the carrier of X
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like non empty total V18([: 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 non empty set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of X . ((seq1 . n),(- (seq2 . n))) is right_complementable Element of the carrier of X
a * ((seq1 . n) - (seq2 . n)) is right_complementable Element of the carrier of X
the Mult of X . (a,((seq1 . n) - (seq2 . n))) is set
a * (seq1 . n) is right_complementable Element of the carrier of X
the Mult of X . (a,(seq1 . n)) is set
a * (seq2 . n) is right_complementable Element of the carrier of X
the Mult of X . (a,(seq2 . n)) is set
(a * (seq1 . n)) - (a * (seq2 . n)) is right_complementable Element of the carrier of X
- (a * (seq2 . n)) is right_complementable Element of the carrier of X
(a * (seq1 . n)) + (- (a * (seq2 . n))) is right_complementable Element of the carrier of X
the addF of X . ((a * (seq1 . n)),(- (a * (seq2 . n)))) is right_complementable Element of the carrier of X
(a * seq1) . n is right_complementable Element of the carrier of X
((a * seq1) . n) - (a * (seq2 . n)) is right_complementable Element of the carrier of X
((a * seq1) . n) + (- (a * (seq2 . n))) is right_complementable Element of the carrier of X
the addF of X . (((a * seq1) . n),(- (a * (seq2 . n)))) is right_complementable Element of the carrier of X
(a * seq2) . n is right_complementable Element of the carrier of X
((a * seq1) . n) - ((a * seq2) . n) is right_complementable Element of the carrier of X
- ((a * seq2) . n) is right_complementable Element of the carrier of X
((a * seq1) . n) + (- ((a * seq2) . n)) is right_complementable Element of the carrier of X
the addF of X . (((a * seq1) . n),(- ((a * seq2) . n))) is right_complementable Element of the carrier of X
((a * seq1) - (a * seq2)) . n is right_complementable Element of the carrier of X