:: VECTSP_4 semantic presentation

K126() is Element of bool K122()
K122() is set
bool K122() is non empty set
K121() is set
bool K121() is non empty set
bool K126() is non empty set
{} is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty set
the Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty set is Relation-like non-empty empty-yielding Function-like one-to-one constant functional empty set
1 is non empty set
GF is non empty right_complementable unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty set
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of GF
u - W is right_complementable Element of the carrier of GF
- W is right_complementable Element of the carrier of GF
u + (- W) is right_complementable Element of the carrier of GF
the addF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the addF of GF . (u,(- W)) is right_complementable Element of the carrier of GF
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of GF . [u,(- W)] is set
B is right_complementable Element of the carrier of V
(u - W) * B is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((u - W),B) is right_complementable Element of the carrier of V
[(u - W),B] is set
{(u - W),B} is non empty set
{(u - W)} is non empty set
{{(u - W),B},{(u - W)}} is non empty set
the lmult of V . [(u - W),B] is set
u * B is right_complementable Element of the carrier of V
the lmult of V . (u,B) is right_complementable Element of the carrier of V
[u,B] is set
{u,B} is non empty set
{{u,B},{u}} is non empty set
the lmult of V . [u,B] is set
W * B is right_complementable Element of the carrier of V
the lmult of V . (W,B) is right_complementable Element of the carrier of V
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the lmult of V . [W,B] is set
(u * B) - (W * B) is right_complementable Element of the carrier of V
- (W * B) is right_complementable Element of the carrier of V
(u * B) + (- (W * B)) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((u * B),(- (W * B))) is right_complementable Element of the carrier of V
[(u * B),(- (W * B))] is set
{(u * B),(- (W * B))} is non empty set
{(u * B)} is non empty set
{{(u * B),(- (W * B))},{(u * B)}} is non empty set
the addF of V . [(u * B),(- (W * B))] is set
(- W) * B is right_complementable Element of the carrier of V
the lmult of V . ((- W),B) is right_complementable Element of the carrier of V
[(- W),B] is set
{(- W),B} is non empty set
{(- W)} is non empty set
{{(- W),B},{(- W)}} is non empty set
the lmult of V . [(- W),B] is set
(u * B) + ((- W) * B) is right_complementable Element of the carrier of V
the addF of V . ((u * B),((- W) * B)) is right_complementable Element of the carrier of V
[(u * B),((- W) * B)] is set
{(u * B),((- W) * B)} is non empty set
{{(u * B),((- W) * B)},{(u * B)}} is non empty set
the addF of V . [(u * B),((- W) * B)] is set
GF is non empty multMagma
V is non empty VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
u is Element of bool the carrier of V
the Element of u is Element of u
0. GF is V49(GF) right_complementable Element of the carrier of GF
the carrier of GF is non empty set
the ZeroF of GF is right_complementable Element of the carrier of GF
B is right_complementable Element of the carrier of V
(0. GF) * B is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((0. GF),B) is right_complementable Element of the carrier of V
[(0. GF),B] is set
{(0. GF),B} is non empty set
{(0. GF)} is non empty set
{{(0. GF),B},{(0. GF)}} is non empty set
the lmult of V . [(0. GF),B] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is Element of bool the carrier of V
W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
1_ GF is right_complementable Element of the carrier of GF
the carrier of GF is non empty set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
- (1_ GF) is right_complementable Element of the carrier of GF
(- (1_ GF)) * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((- (1_ GF)),W) is right_complementable Element of the carrier of V
[(- (1_ GF)),W] is set
{(- (1_ GF)),W} is non empty set
{(- (1_ GF))} is non empty set
{{(- (1_ GF)),W},{(- (1_ GF))}} is non empty set
the lmult of V . [(- (1_ GF)),W] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is Element of bool the carrier of V
W is right_complementable Element of the carrier of V
B is right_complementable Element of the carrier of V
W - B is right_complementable Element of the carrier of V
- B is right_complementable Element of the carrier of V
W + (- B) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,(- B)) is right_complementable Element of the carrier of V
[W,(- B)] is set
{W,(- B)} is non empty set
{W} is non empty set
{{W,(- B)},{W}} is non empty set
the addF of V . [W,(- B)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u + W is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the addF of V . [u,W] is set
the carrier of GF is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is Element of bool the carrier of V
W is right_complementable Element of the carrier of V
B is right_complementable Element of the carrier of V
W + B is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,B) is right_complementable Element of the carrier of V
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the addF of V . [W,B] is set
the carrier of GF is non empty set
W is right_complementable Element of the carrier of GF
B is right_complementable Element of the carrier of V
W * B is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (W,B) is right_complementable Element of the carrier of V
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the lmult of V . [W,B] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is Element of bool the carrier of V
W is Element of bool the carrier of V
B is Element of bool the carrier of V
{ (b₁ + b₂) where b₁, b₂ is right_complementable Element of the carrier of V : ( b₁ in u & b₂ in W ) } is set
C is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
C + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (C,C) is right_complementable Element of the carrier of V
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the addF of V . [C,C] is set
c₈ is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
c₈ + x is right_complementable Element of the carrier of V
the addF of V . (c₈,x) is right_complementable Element of the carrier of V
[c₈,x] is set
{c₈,x} is non empty set
{c₈} is non empty set
{{c₈,x},{c₈}} is non empty set
the addF of V . [c₈,x] is set
x is right_complementable Element of the carrier of V
z is right_complementable Element of the carrier of V
x + z is right_complementable Element of the carrier of V
the addF of V . (x,z) is right_complementable Element of the carrier of V
[x,z] is set
{x,z} is non empty set
{x} is non empty set
{{x,z},{x}} is non empty set
the addF of V . [x,z] is set
(c₈ + x) + x is right_complementable Element of the carrier of V
the addF of V . ((c₈ + x),x) is right_complementable Element of the carrier of V
[(c₈ + x),x] is set
{(c₈ + x),x} is non empty set
{(c₈ + x)} is non empty set
{{(c₈ + x),x},{(c₈ + x)}} is non empty set
the addF of V . [(c₈ + x),x] is set
((c₈ + x) + x) + z is right_complementable Element of the carrier of V
the addF of V . (((c₈ + x) + x),z) is right_complementable Element of the carrier of V
[((c₈ + x) + x),z] is set
{((c₈ + x) + x),z} is non empty set
{((c₈ + x) + x)} is non empty set
{{((c₈ + x) + x),z},{((c₈ + x) + x)}} is non empty set
the addF of V . [((c₈ + x) + x),z] is set
c₈ + x is right_complementable Element of the carrier of V
the addF of V . (c₈,x) is right_complementable Element of the carrier of V
[c₈,x] is set
{c₈,x} is non empty set
{{c₈,x},{c₈}} is non empty set
the addF of V . [c₈,x] is set
(c₈ + x) + x is right_complementable Element of the carrier of V
the addF of V . ((c₈ + x),x) is right_complementable Element of the carrier of V
[(c₈ + x),x] is set
{(c₈ + x),x} is non empty set
{(c₈ + x)} is non empty set
{{(c₈ + x),x},{(c₈ + x)}} is non empty set
the addF of V . [(c₈ + x),x] is set
((c₈ + x) + x) + z is right_complementable Element of the carrier of V
the addF of V . (((c₈ + x) + x),z) is right_complementable Element of the carrier of V
[((c₈ + x) + x),z] is set
{((c₈ + x) + x),z} is non empty set
{((c₈ + x) + x)} is non empty set
{{((c₈ + x) + x),z},{((c₈ + x) + x)}} is non empty set
the addF of V . [((c₈ + x) + x),z] is set
x + z is right_complementable Element of the carrier of V
the addF of V . (x,z) is right_complementable Element of the carrier of V
[x,z] is set
{x,z} is non empty set
{x} is non empty set
{{x,z},{x}} is non empty set
the addF of V . [x,z] is set
(c₈ + x) + (x + z) is right_complementable Element of the carrier of V
the addF of V . ((c₈ + x),(x + z)) is right_complementable Element of the carrier of V
[(c₈ + x),(x + z)] is set
{(c₈ + x),(x + z)} is non empty set
{{(c₈ + x),(x + z)},{(c₈ + x)}} is non empty set
the addF of V . [(c₈ + x),(x + z)] is set
the carrier of GF is non empty set
C is right_complementable Element of the carrier of GF
C is right_complementable Element of the carrier of V
C * C is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (C,C) is right_complementable Element of the carrier of V
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the lmult of V . [C,C] is set
c₈ is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
c₈ + x is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (c₈,x) is right_complementable Element of the carrier of V
[c₈,x] is set
{c₈,x} is non empty set
{c₈} is non empty set
{{c₈,x},{c₈}} is non empty set
the addF of V . [c₈,x] is set
C * c₈ is right_complementable Element of the carrier of V
the lmult of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{{C,c₈},{C}} is non empty set
the lmult of V . [C,c₈] is set
C * x is right_complementable Element of the carrier of V
the lmult of V . (C,x) is right_complementable Element of the carrier of V
[C,x] is set
{C,x} is non empty set
{{C,x},{C}} is non empty set
the lmult of V . [C,x] is set
(C * c₈) + (C * x) is right_complementable Element of the carrier of V
the addF of V . ((C * c₈),(C * x)) is right_complementable Element of the carrier of V
[(C * c₈),(C * x)] is set
{(C * c₈),(C * x)} is non empty set
{(C * c₈)} is non empty set
{{(C * c₈),(C * x)},{(C * c₈)}} is non empty set
the addF of V . [(C * c₈),(C * x)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is Element of bool the carrier of V
W is Element of bool the carrier of V
u /\ W is Element of bool the carrier of V
B is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
B + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (B,C) is right_complementable Element of the carrier of V
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of V . [B,C] is set
the carrier of GF is non empty set
B is right_complementable Element of the carrier of GF
C is right_complementable Element of the carrier of V
B * C is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (B,C) is right_complementable Element of the carrier of V
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the lmult of V . [B,C] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the addF of V || the carrier of V is Relation-like Function-like set
the addF of V | [: the carrier of V, the carrier of V:] is Relation-like Function-like set
the lmult of V | [: the carrier of GF, the carrier of V:] is Relation-like Function-like set
GF is set
V is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (V,u)
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (V,u)
the carrier of W is non empty set
the carrier of B is non empty set
GF is set
V is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (V,u)
the carrier of W is non empty set
the carrier of u is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is right_complementable Element of the carrier of u
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. u is V49(u) right_complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is right_complementable Element of the carrier of u
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. u is V49(u) right_complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is right_complementable Element of the carrier of u
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. W is V49(W) right_complementable Element of the carrier of W
the carrier of W is non empty set
the ZeroF of W is right_complementable Element of the carrier of W
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u + W is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the addF of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of B is non empty set
C is right_complementable Element of the carrier of B
C is right_complementable Element of the carrier of B
C + C is right_complementable Element of the carrier of B
the addF of B is Relation-like Function-like V18([: the carrier of B, the carrier of B:], the carrier of B) Element of bool [:[: the carrier of B, the carrier of B:], the carrier of B:]
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of B, the carrier of B:], the carrier of B:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:], the carrier of B:] is non empty set
the addF of B . (C,C) is right_complementable Element of the carrier of B
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the addF of B . [C,C] is set
the addF of V || the carrier of B is Relation-like Function-like set
the addF of V | [: the carrier of B, the carrier of B:] is Relation-like Function-like set
[C,C] is Element of [: the carrier of B, the carrier of B:]
( the addF of V || the carrier of B) . [C,C] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty set
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of B is non empty set
C is right_complementable Element of the carrier of B
u * C is right_complementable Element of the carrier of B
the lmult of B is Relation-like Function-like V18([: the carrier of GF, the carrier of B:], the carrier of B) Element of bool [:[: the carrier of GF, the carrier of B:], the carrier of B:]
[: the carrier of GF, the carrier of B:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of B:], the carrier of B:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of B:], the carrier of B:] is non empty set
the lmult of B . (u,C) is right_complementable Element of the carrier of B
[u,C] is set
{u,C} is non empty set
{{u,C},{u}} is non empty set
the lmult of B . [u,C] is set
the lmult of V | [: the carrier of GF, the carrier of B:] is Relation-like Function-like set
[u,C] is Element of [: the carrier of GF, the carrier of B:]
( the lmult of V | [: the carrier of GF, the carrier of B:]) . [u,C] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of W is non empty set
B is right_complementable Element of the carrier of W
- B is right_complementable Element of the carrier of W
1_ GF is right_complementable Element of the carrier of GF
the carrier of GF is non empty set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
- (1_ GF) is right_complementable Element of the carrier of GF
(- (1_ GF)) * u is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((- (1_ GF)),u) is right_complementable Element of the carrier of V
[(- (1_ GF)),u] is set
{(- (1_ GF)),u} is non empty set
{(- (1_ GF))} is non empty set
{{(- (1_ GF)),u},{(- (1_ GF))}} is non empty set
the lmult of V . [(- (1_ GF)),u] is set
(- (1_ GF)) * B is right_complementable Element of the carrier of W
the lmult of W is Relation-like Function-like V18([: the carrier of GF, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of GF, the carrier of W:], the carrier of W:]
[: the carrier of GF, the carrier of W:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of W:], the carrier of W:] is non empty set
the lmult of W . ((- (1_ GF)),B) is right_complementable Element of the carrier of W
[(- (1_ GF)),B] is set
{(- (1_ GF)),B} is non empty set
{{(- (1_ GF)),B},{(- (1_ GF))}} is non empty set
the lmult of W . [(- (1_ GF)),B] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
u + (- W) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(- W)) is right_complementable Element of the carrier of V
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of V . [u,(- W)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of B is non empty set
C is right_complementable Element of the carrier of B
C is right_complementable Element of the carrier of B
C - C is right_complementable Element of the carrier of B
- C is right_complementable Element of the carrier of B
C + (- C) is right_complementable Element of the carrier of B
the addF of B is Relation-like Function-like V18([: the carrier of B, the carrier of B:], the carrier of B) Element of bool [:[: the carrier of B, the carrier of B:], the carrier of B:]
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of B, the carrier of B:], the carrier of B:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:], the carrier of B:] is non empty set
the addF of B . (C,(- C)) is right_complementable Element of the carrier of B
[C,(- C)] is set
{C,(- C)} is non empty set
{C} is non empty set
{{C,(- C)},{C}} is non empty set
the addF of B . [C,(- C)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is Element of bool the carrier of V
C is right_complementable Element of the carrier of V
c₈ is right_complementable Element of the carrier of V
C + c₈ is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
C is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of C is non empty set
x is right_complementable Element of the carrier of C
x is right_complementable Element of the carrier of C
x + x is right_complementable Element of the carrier of C
the addF of C is Relation-like Function-like V18([: the carrier of C, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of C, the carrier of C:], the carrier of C:]
[: the carrier of C, the carrier of C:] is Relation-like non empty set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is Relation-like non empty set
bool [:[: the carrier of C, the carrier of C:], the carrier of C:] is non empty set
the addF of C . (x,x) is right_complementable Element of the carrier of C
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
the addF of C . [x,x] is set
z is right_complementable Element of the carrier of u
the carrier of GF is non empty set
C is right_complementable Element of the carrier of GF
c₈ is right_complementable Element of the carrier of V
C * c₈ is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the lmult of V . [C,c₈] is set
C is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of C is non empty set
x is right_complementable Element of the carrier of C
C * x is right_complementable Element of the carrier of C
the lmult of C is Relation-like Function-like V18([: the carrier of GF, the carrier of C:], the carrier of C) Element of bool [:[: the carrier of GF, the carrier of C:], the carrier of C:]
[: the carrier of GF, the carrier of C:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of C:], the carrier of C:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of C:], the carrier of C:] is non empty set
the lmult of C . (C,x) is right_complementable Element of the carrier of C
[C,x] is set
{C,x} is non empty set
{{C,x},{C}} is non empty set
the lmult of C . [C,x] is set
x is right_complementable Element of the carrier of u
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. u is V49(u) right_complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is right_complementable Element of the carrier of u
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. u is V49(u) right_complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is right_complementable Element of the carrier of u
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
0. u is V49(u) right_complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is right_complementable Element of the carrier of u
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u + W is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the addF of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
bool the carrier of V is non empty set
the carrier of B is non empty set
C is Element of bool the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty set
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
bool the carrier of V is non empty set
the carrier of B is non empty set
C is Element of bool the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
1_ GF is right_complementable Element of the carrier of GF
the carrier of GF is non empty set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
- (1_ GF) is right_complementable Element of the carrier of GF
(- (1_ GF)) * u is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((- (1_ GF)),u) is right_complementable Element of the carrier of V
[(- (1_ GF)),u] is set
{(- (1_ GF)),u} is non empty set
{(- (1_ GF))} is non empty set
{{(- (1_ GF)),u},{(- (1_ GF))}} is non empty set
the lmult of V . [(- (1_ GF)),u] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
u + (- W) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(- W)) is right_complementable Element of the carrier of V
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of V . [u,(- W)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
the carrier of V is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V | [: the carrier of GF, the carrier of V:] is Relation-like Function-like set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V || the carrier of V is Relation-like Function-like set
the addF of V | [: the carrier of V, the carrier of V:] is Relation-like Function-like set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
V is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
the carrier of u is non empty set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of u is Relation-like Function-like V18([: the carrier of u, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of u, the carrier of u:], the carrier of u:]
[: the carrier of u, the carrier of u:] is Relation-like non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of V || the carrier of u is Relation-like Function-like set
the addF of V | [: the carrier of u, the carrier of u:] is Relation-like Function-like set
the addF of u || the carrier of V is Relation-like Function-like set
the addF of u | [: the carrier of V, the carrier of V:] is Relation-like Function-like set
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of u is Relation-like Function-like V18([: the carrier of GF, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of GF, the carrier of u:], the carrier of u:]
[: the carrier of GF, the carrier of u:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of u:], the carrier of u:] is non empty set
the lmult of u | [: the carrier of GF, the carrier of V:] is Relation-like Function-like set
0. u is V49(u) right_complementable Element of the carrier of u
the ZeroF of u is right_complementable Element of the carrier of u
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
the lmult of V | [: the carrier of GF, the carrier of u:] is Relation-like Function-like set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
the carrier of u is non empty set
the carrier of W is non empty set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of W is Relation-like Function-like V18([: the carrier of W, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of W, the carrier of W:], the carrier of W:]
[: the carrier of W, the carrier of W:] is Relation-like non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of W, the carrier of W:], the carrier of W:] is non empty set
the addF of W || the carrier of V is Relation-like Function-like set
the addF of W | [: the carrier of V, the carrier of V:] is Relation-like Function-like set
the addF of u is Relation-like Function-like V18([: the carrier of u, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of u, the carrier of u:], the carrier of u:]
[: the carrier of u, the carrier of u:] is Relation-like non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of u || the carrier of V is Relation-like Function-like set
the addF of u | [: the carrier of V, the carrier of V:] is Relation-like Function-like set
the addF of W || the carrier of u is Relation-like Function-like set
the addF of W | [: the carrier of u, the carrier of u:] is Relation-like Function-like set
( the addF of W || the carrier of u) || the carrier of V is Relation-like Function-like set
( the addF of W || the carrier of u) | [: the carrier of V, the carrier of V:] is Relation-like Function-like set
the lmult of W is Relation-like Function-like V18([: the carrier of GF, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of GF, the carrier of W:], the carrier of W:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of W:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of W:], the carrier of W:] is non empty set
the lmult of u is Relation-like Function-like V18([: the carrier of GF, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of GF, the carrier of u:], the carrier of u:]
[: the carrier of GF, the carrier of u:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of u:], the carrier of u:] is non empty set
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of u | [: the carrier of GF, the carrier of V:] is Relation-like Function-like set
the lmult of W | [: the carrier of GF, the carrier of u:] is Relation-like Function-like set
( the lmult of W | [: the carrier of GF, the carrier of u:]) | [: the carrier of GF, the carrier of V:] is Relation-like Function-like set
the lmult of W | [: the carrier of GF, the carrier of V:] is Relation-like Function-like set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
0. u is V49(u) right_complementable Element of the carrier of u
the ZeroF of u is right_complementable Element of the carrier of u
0. W is V49(W) right_complementable Element of the carrier of W
the ZeroF of W is right_complementable Element of the carrier of W
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of W is non empty set
the lmult of u is Relation-like Function-like V18([: the carrier of GF, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of GF, the carrier of u:], the carrier of u:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of u:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of u:], the carrier of u:] is non empty set
the lmult of W is Relation-like Function-like V18([: the carrier of GF, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of GF, the carrier of W:], the carrier of W:]
[: the carrier of GF, the carrier of W:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of W:], the carrier of W:] is non empty set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the addF of u is Relation-like Function-like V18([: the carrier of u, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of u, the carrier of u:], the carrier of u:]
[: the carrier of u, the carrier of u:] is Relation-like non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of V || the carrier of u is Relation-like Function-like set
the addF of V | [: the carrier of u, the carrier of u:] is Relation-like Function-like set
the addF of W is Relation-like Function-like V18([: the carrier of W, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of W, the carrier of W:], the carrier of W:]
[: the carrier of W, the carrier of W:] is Relation-like non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of W, the carrier of W:], the carrier of W:] is non empty set
the addF of V || the carrier of W is Relation-like Function-like set
the addF of V | [: the carrier of W, the carrier of W:] is Relation-like Function-like set
the addF of W || the carrier of u is Relation-like Function-like set
the addF of W | [: the carrier of u, the carrier of u:] is Relation-like Function-like set
the lmult of V | [: the carrier of GF, the carrier of u:] is Relation-like Function-like set
the lmult of V | [: the carrier of GF, the carrier of W:] is Relation-like Function-like set
the lmult of W | [: the carrier of GF, the carrier of u:] is Relation-like Function-like set
0. u is V49(u) right_complementable Element of the carrier of u
the ZeroF of u is right_complementable Element of the carrier of u
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
0. W is V49(W) right_complementable Element of the carrier of W
the ZeroF of W is right_complementable Element of the carrier of W
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
the carrier of W is non empty set
B is set
C is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
the carrier of V is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is non empty strict VectSpStr over GF
the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is non empty set
B is right_complementable Element of the carrier of GF
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
C + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (C,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [C,C] is set
B * (C + C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,(C + C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,(C + C)] is set
{B,(C + C)} is non empty set
{B} is non empty set
{{B,(C + C)},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,(C + C)] is set
B * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
B * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
(B * C) + (B * C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((B * C),(B * C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(B * C),(B * C)] is set
{(B * C),(B * C)} is non empty set
{(B * C)} is non empty set
{{(B * C),(B * C)},{(B * C)}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(B * C),(B * C)] is set
c₈ is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
c₈ + x is right_complementable Element of the carrier of V
the addF of V . (c₈,x) is right_complementable Element of the carrier of V
[c₈,x] is set
{c₈,x} is non empty set
{c₈} is non empty set
{{c₈,x},{c₈}} is non empty set
the addF of V . [c₈,x] is set
B * (c₈ + x) is right_complementable Element of the carrier of V
the lmult of V . (B,(c₈ + x)) is right_complementable Element of the carrier of V
[B,(c₈ + x)] is set
{B,(c₈ + x)} is non empty set
{{B,(c₈ + x)},{B}} is non empty set
the lmult of V . [B,(c₈ + x)] is set
B * c₈ is right_complementable Element of the carrier of V
the lmult of V . (B,c₈) is right_complementable Element of the carrier of V
[B,c₈] is set
{B,c₈} is non empty set
{{B,c₈},{B}} is non empty set
the lmult of V . [B,c₈] is set
B * x is right_complementable Element of the carrier of V
the lmult of V . (B,x) is right_complementable Element of the carrier of V
[B,x] is set
{B,x} is non empty set
{{B,x},{B}} is non empty set
the lmult of V . [B,x] is set
(B * c₈) + (B * x) is right_complementable Element of the carrier of V
the addF of V . ((B * c₈),(B * x)) is right_complementable Element of the carrier of V
[(B * c₈),(B * x)] is set
{(B * c₈),(B * x)} is non empty set
{(B * c₈)} is non empty set
{{(B * c₈),(B * x)},{(B * c₈)}} is non empty set
the addF of V . [(B * c₈),(B * x)] is set
the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is non empty set
B is right_complementable Element of the carrier of GF
C is right_complementable Element of the carrier of GF
B + C is right_complementable Element of the carrier of GF
the addF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the addF of GF . (B,C) is right_complementable Element of the carrier of GF
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of GF . [B,C] is set
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
(B + C) * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((B + C),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(B + C),C] is set
{(B + C),C} is non empty set
{(B + C)} is non empty set
{{(B + C),C},{(B + C)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(B + C),C] is set
B * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
C * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (C,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [C,C] is set
(B * C) + (C * C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((B * C),(C * C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(B * C),(C * C)] is set
{(B * C),(C * C)} is non empty set
{(B * C)} is non empty set
{{(B * C),(C * C)},{(B * C)}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(B * C),(C * C)] is set
B + C is right_complementable Element of the carrier of GF
(B + C) * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((B + C),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(B + C),C] is set
{(B + C),C} is non empty set
{(B + C)} is non empty set
{{(B + C),C},{(B + C)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(B + C),C] is set
c₈ is right_complementable Element of the carrier of V
(B + C) * c₈ is right_complementable Element of the carrier of V
the lmult of V . ((B + C),c₈) is right_complementable Element of the carrier of V
[(B + C),c₈] is set
{(B + C),c₈} is non empty set
{{(B + C),c₈},{(B + C)}} is non empty set
the lmult of V . [(B + C),c₈] is set
B * c₈ is right_complementable Element of the carrier of V
the lmult of V . (B,c₈) is right_complementable Element of the carrier of V
[B,c₈] is set
{B,c₈} is non empty set
{{B,c₈},{B}} is non empty set
the lmult of V . [B,c₈] is set
C * c₈ is right_complementable Element of the carrier of V
the lmult of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{{C,c₈},{C}} is non empty set
the lmult of V . [C,c₈] is set
(B * c₈) + (C * c₈) is right_complementable Element of the carrier of V
the addF of V . ((B * c₈),(C * c₈)) is right_complementable Element of the carrier of V
[(B * c₈),(C * c₈)] is set
{(B * c₈),(C * c₈)} is non empty set
{(B * c₈)} is non empty set
{{(B * c₈),(C * c₈)},{(B * c₈)}} is non empty set
the addF of V . [(B * c₈),(C * c₈)] is set
the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is non empty set
B is right_complementable Element of the carrier of GF
C is right_complementable Element of the carrier of GF
B * C is right_complementable Element of the carrier of GF
the multF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the multF of GF . (B,C) is right_complementable Element of the carrier of GF
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the multF of GF . [B,C] is set
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
(B * C) * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((B * C),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(B * C),C] is set
{(B * C),C} is non empty set
{(B * C)} is non empty set
{{(B * C),C},{(B * C)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(B * C),C] is set
C * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (C,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [C,C] is set
B * (C * C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,(C * C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,(C * C)] is set
{B,(C * C)} is non empty set
{{B,(C * C)},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,(C * C)] is set
c₈ is right_complementable Element of the carrier of V
(B * C) * c₈ is right_complementable Element of the carrier of V
the lmult of V . ((B * C),c₈) is right_complementable Element of the carrier of V
[(B * C),c₈] is set
{(B * C),c₈} is non empty set
{{(B * C),c₈},{(B * C)}} is non empty set
the lmult of V . [(B * C),c₈] is set
C * c₈ is right_complementable Element of the carrier of V
the lmult of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{{C,c₈},{C}} is non empty set
the lmult of V . [C,c₈] is set
B * (C * c₈) is right_complementable Element of the carrier of V
the lmult of V . (B,(C * c₈)) is right_complementable Element of the carrier of V
[B,(C * c₈)] is set
{B,(C * c₈)} is non empty set
{{B,(C * c₈)},{B}} is non empty set
the lmult of V . [B,(C * c₈)] is set
the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is non empty set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
(1. GF) * B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((1. GF),B) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(1. GF),B] is set
{(1. GF),B} is non empty set
{(1. GF)} is non empty set
{{(1. GF),B},{(1. GF)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(1. GF),B] is set
1_ GF is right_complementable Element of the carrier of GF
C is right_complementable Element of the carrier of V
(1_ GF) * C is right_complementable Element of the carrier of V
the lmult of V . ((1_ GF),C) is right_complementable Element of the carrier of V
[(1_ GF),C] is set
{(1_ GF),C} is non empty set
{(1_ GF)} is non empty set
{{(1_ GF),C},{(1_ GF)}} is non empty set
the lmult of V . [(1_ GF),C] is set
the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is non empty set
C is right_complementable Element of the carrier of V
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
c₈ is right_complementable Element of the carrier of V
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
C + c₈ is right_complementable Element of the carrier of V
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
C + B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (C,B) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[C,B] is set
{C,B} is non empty set
{C} is non empty set
{{C,B},{C}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [C,B] is set
c₈ is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
c₈ + C is right_complementable Element of the carrier of V
the addF of V . (c₈,C) is right_complementable Element of the carrier of V
[c₈,C] is set
{c₈,C} is non empty set
{c₈} is non empty set
{{c₈,C},{c₈}} is non empty set
the addF of V . [c₈,C] is set
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
(B + C) + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . ((B + C),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[(B + C),C] is set
{(B + C),C} is non empty set
{(B + C)} is non empty set
{{(B + C),C},{(B + C)}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [(B + C),C] is set
c₈ is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
c₈ + x is right_complementable Element of the carrier of V
the addF of V . (c₈,x) is right_complementable Element of the carrier of V
[c₈,x] is set
{c₈,x} is non empty set
{c₈} is non empty set
{{c₈,x},{c₈}} is non empty set
the addF of V . [c₈,x] is set
x is right_complementable Element of the carrier of V
(c₈ + x) + x is right_complementable Element of the carrier of V
the addF of V . ((c₈ + x),x) is right_complementable Element of the carrier of V
[(c₈ + x),x] is set
{(c₈ + x),x} is non empty set
{(c₈ + x)} is non empty set
{{(c₈ + x),x},{(c₈ + x)}} is non empty set
the addF of V . [(c₈ + x),x] is set
x + x is right_complementable Element of the carrier of V
the addF of V . (x,x) is right_complementable Element of the carrier of V
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
the addF of V . [x,x] is set
c₈ + (x + x) is right_complementable Element of the carrier of V
the addF of V . (c₈,(x + x)) is right_complementable Element of the carrier of V
[c₈,(x + x)] is set
{c₈,(x + x)} is non empty set
{{c₈,(x + x)},{c₈}} is non empty set
the addF of V . [c₈,(x + x)] is set
C + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (C,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [C,C] is set
B + (C + C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,(C + C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,(C + C)] is set
{B,(C + C)} is non empty set
{{B,(C + C)},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,(C + C)] is set
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is V49( VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the ZeroF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
B + (0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,(0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #))) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,(0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #))] is set
{B,(0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #))} is non empty set
{B} is non empty set
{{B,(0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #))},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,(0. VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #))] is set
C is right_complementable Element of the carrier of V
C + (0. V) is right_complementable Element of the carrier of V
the addF of V . (C,(0. V)) is right_complementable Element of the carrier of V
[C,(0. V)] is set
{C,(0. V)} is non empty set
{C} is non empty set
{{C,(0. V)},{C}} is non empty set
the addF of V . [C,(0. V)] is set
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
comp V is Relation-like Function-like V18( the carrier of V, the carrier of V) Element of bool [: the carrier of V, the carrier of V:]
bool [: the carrier of V, the carrier of V:] is non empty set
C is right_complementable Element of the carrier of V
(comp V) . C is right_complementable Element of the carrier of V
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V,(0. V), the lmult of V #) . [B,C] is set
- C is right_complementable Element of the carrier of V
C + (- C) is right_complementable Element of the carrier of V
the addF of V . (C,(- C)) is right_complementable Element of the carrier of V
[C,(- C)] is set
{C,(- C)} is non empty set
{C} is non empty set
{{C,(- C)},{C}} is non empty set
the addF of V . [C,(- C)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
0. B is V49(B) right_complementable Element of the carrier of B
the carrier of B is non empty set
the ZeroF of B is right_complementable Element of the carrier of B
the addF of B is Relation-like Function-like V18([: the carrier of B, the carrier of B:], the carrier of B) Element of bool [:[: the carrier of B, the carrier of B:], the carrier of B:]
[: the carrier of B, the carrier of B:] is Relation-like non empty set
[:[: the carrier of B, the carrier of B:], the carrier of B:] is Relation-like non empty set
bool [:[: the carrier of B, the carrier of B:], the carrier of B:] is non empty set
the addF of V || the carrier of B is Relation-like Function-like set
the addF of V | [: the carrier of B, the carrier of B:] is Relation-like Function-like set
the lmult of B is Relation-like Function-like V18([: the carrier of GF, the carrier of B:], the carrier of B) Element of bool [:[: the carrier of GF, the carrier of B:], the carrier of B:]
[: the carrier of GF, the carrier of B:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of B:], the carrier of B:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of B:], the carrier of B:] is non empty set
the lmult of V | [: the carrier of GF, the carrier of B:] is Relation-like Function-like set
C is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of W is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
W is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
the carrier of W is non empty set
B is set
C is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
W is right_complementable Element of the carrier of V
B is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is Element of bool the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is Element of bool the carrier of V
W is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
comp V is Relation-like Function-like V18( the carrier of V, the carrier of V) Element of bool [: the carrier of V, the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
bool [: the carrier of V, the carrier of V:] is non empty set
(comp V) | W is Relation-like Function-like set
dom (comp V) is set
dom ((comp V) | W) is set
rng ((comp V) | W) is set
c₈ is set
x is set
((comp V) | W) . x is set
x is right_complementable Element of the carrier of V
(comp V) . x is right_complementable Element of the carrier of V
- x is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
[: the carrier of GF,W:] is Relation-like non empty set
the lmult of V | [: the carrier of GF,W:] is Relation-like Function-like set
dom the lmult of V is set
dom ( the lmult of V | [: the carrier of GF,W:]) is set
rng ( the lmult of V | [: the carrier of GF,W:]) is set
x is set
x is set
( the lmult of V | [: the carrier of GF,W:]) . x is set
z is set
u1 is set
[z,u1] is set
{z,u1} is non empty set
{z} is non empty set
{{z,u1},{z}} is non empty set
W is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
W * W is right_complementable Element of the carrier of V
the lmult of V . (W,W) is right_complementable Element of the carrier of V
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the lmult of V . [W,W] is set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V || W is Relation-like Function-like set
[:W,W:] is Relation-like non empty set
the addF of V | [:W,W:] is Relation-like Function-like set
dom the addF of V is set
dom ( the addF of V || W) is set
rng ( the addF of V || W) is set
x is set
z is set
( the addF of V || W) . z is set
u1 is set
W is set
[u1,W] is set
{u1,W} is non empty set
{u1} is non empty set
{{u1,W},{u1}} is non empty set
W is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
W + W is right_complementable Element of the carrier of V
the addF of V . (W,W) is right_complementable Element of the carrier of V
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the addF of V . [W,W] is set
[:[: the carrier of GF,W:],W:] is Relation-like non empty set
bool [:[: the carrier of GF,W:],W:] is non empty set
bool [:W,W:] is non empty set
[:[:W,W:],W:] is Relation-like non empty set
bool [:[:W,W:],W:] is non empty set
u1 is Relation-like Function-like V18([:W,W:],W) Element of bool [:[:W,W:],W:]
B is Element of W
x is Relation-like Function-like V18([: the carrier of GF,W:],W) Element of bool [:[: the carrier of GF,W:],W:]
VectSpStr(# W,u1,B,x #) is non empty strict VectSpStr over GF
the carrier of VectSpStr(# W,u1,B,x #) is non empty set
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
W + W is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the addF of VectSpStr(# W,u1,B,x #) . (W,W) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,W] is set
c₁₆ is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
c₁₆ + x is right_complementable Element of the carrier of V
the addF of V . (c₁₆,x) is right_complementable Element of the carrier of V
[c₁₆,x] is set
{c₁₆,x} is non empty set
{c₁₆} is non empty set
{{c₁₆,x},{c₁₆}} is non empty set
the addF of V . [c₁₆,x] is set
[W,W] is Element of [: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):]
u1 . [W,W] is set
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
W + W is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the addF of VectSpStr(# W,u1,B,x #) . (W,W) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,W] is set
W + W is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . (W,W) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,W] is set
x is right_complementable Element of the carrier of V
c₁₆ is right_complementable Element of the carrier of V
x + c₁₆ is right_complementable Element of the carrier of V
the addF of V . (x,c₁₆) is right_complementable Element of the carrier of V
[x,c₁₆] is set
{x,c₁₆} is non empty set
{x} is non empty set
{{x,c₁₆},{x}} is non empty set
the addF of V . [x,c₁₆] is set
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
W + c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the addF of VectSpStr(# W,u1,B,x #) . (W,c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,c₁₆] is set
{W,c₁₆} is non empty set
{W} is non empty set
{{W,c₁₆},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,c₁₆] is set
y is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
y + x is right_complementable Element of the carrier of V
the addF of V . (y,x) is right_complementable Element of the carrier of V
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
the addF of V . [y,x] is set
W + W is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . (W,W) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,W] is set
x is right_complementable Element of the carrier of V
x + y is right_complementable Element of the carrier of V
the addF of V . (x,y) is right_complementable Element of the carrier of V
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of V . [x,y] is set
(W + W) + c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . ((W + W),c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(W + W),c₁₆] is set
{(W + W),c₁₆} is non empty set
{(W + W)} is non empty set
{{(W + W),c₁₆},{(W + W)}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [(W + W),c₁₆] is set
(x + y) + x is right_complementable Element of the carrier of V
the addF of V . ((x + y),x) is right_complementable Element of the carrier of V
[(x + y),x] is set
{(x + y),x} is non empty set
{(x + y)} is non empty set
{{(x + y),x},{(x + y)}} is non empty set
the addF of V . [(x + y),x] is set
x + (y + x) is right_complementable Element of the carrier of V
the addF of V . (x,(y + x)) is right_complementable Element of the carrier of V
[x,(y + x)] is set
{x,(y + x)} is non empty set
{{x,(y + x)},{x}} is non empty set
the addF of V . [x,(y + x)] is set
W + (W + c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . (W,(W + c₁₆)) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,(W + c₁₆)] is set
{W,(W + c₁₆)} is non empty set
{{W,(W + c₁₆)},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,(W + c₁₆)] is set
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
0. VectSpStr(# W,u1,B,x #) is V49( VectSpStr(# W,u1,B,x #)) Element of the carrier of VectSpStr(# W,u1,B,x #)
the ZeroF of VectSpStr(# W,u1,B,x #) is Element of the carrier of VectSpStr(# W,u1,B,x #)
W + (0. VectSpStr(# W,u1,B,x #)) is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . (W,(0. VectSpStr(# W,u1,B,x #))) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,(0. VectSpStr(# W,u1,B,x #))] is set
{W,(0. VectSpStr(# W,u1,B,x #))} is non empty set
{W} is non empty set
{{W,(0. VectSpStr(# W,u1,B,x #))},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,(0. VectSpStr(# W,u1,B,x #))] is set
W is right_complementable Element of the carrier of V
W + (0. V) is right_complementable Element of the carrier of V
the addF of V . (W,(0. V)) is right_complementable Element of the carrier of V
[W,(0. V)] is set
{W,(0. V)} is non empty set
{W} is non empty set
{{W,(0. V)},{W}} is non empty set
the addF of V . [W,(0. V)] is set
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
z is Relation-like Function-like V18(W,W) Element of bool [:W,W:]
c₁₆ is Element of W
z . c₁₆ is Element of W
x is Element of W
y is Element of the carrier of VectSpStr(# W,u1,B,x #)
W + y is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . (W,y) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,y] is set
{W,y} is non empty set
{W} is non empty set
{{W,y},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,y] is set
W is right_complementable Element of the carrier of V
(comp V) . W is right_complementable Element of the carrier of V
W + ((comp V) . W) is right_complementable Element of the carrier of V
the addF of V . (W,((comp V) . W)) is right_complementable Element of the carrier of V
[W,((comp V) . W)] is set
{W,((comp V) . W)} is non empty set
{W} is non empty set
{{W,((comp V) . W)},{W}} is non empty set
the addF of V . [W,((comp V) . W)] is set
- W is right_complementable Element of the carrier of V
W + (- W) is right_complementable Element of the carrier of V
the addF of V . (W,(- W)) is right_complementable Element of the carrier of V
[W,(- W)] is set
{W,(- W)} is non empty set
{{W,(- W)},{W}} is non empty set
the addF of V . [W,(- W)] is set
W is right_complementable Element of the carrier of GF
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
W + c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the addF of VectSpStr(# W,u1,B,x #) . (W,c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,c₁₆] is set
{W,c₁₆} is non empty set
{W} is non empty set
{{W,c₁₆},{W}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [W,c₁₆] is set
W * (W + c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . (W,(W + c₁₆)) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,(W + c₁₆)] is set
{W,(W + c₁₆)} is non empty set
{W} is non empty set
{{W,(W + c₁₆)},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,(W + c₁₆)] is set
W * W is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (W,W) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,W] is set
{W,W} is non empty set
{{W,W},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,W] is set
W * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (W,c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,c₁₆] is set
{W,c₁₆} is non empty set
{{W,c₁₆},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,c₁₆] is set
(W * W) + (W * c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) . ((W * W),(W * c₁₆)) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(W * W),(W * c₁₆)] is set
{(W * W),(W * c₁₆)} is non empty set
{(W * W)} is non empty set
{{(W * W),(W * c₁₆)},{(W * W)}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [(W * W),(W * c₁₆)] is set
y is right_complementable Element of the carrier of V
y is Element of the carrier of VectSpStr(# W,u1,B,x #)
x is right_complementable Element of the carrier of GF
[x,y] is Element of [: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):]
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
dom x is set
x * y is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (x,y) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[x,y] is set
the lmult of VectSpStr(# W,u1,B,x #) . [x,y] is set
x * y is right_complementable Element of the carrier of V
the lmult of V . (x,y) is right_complementable Element of the carrier of V
[x,y] is set
{x,y} is non empty set
{{x,y},{x}} is non empty set
the lmult of V . [x,y] is set
x is right_complementable Element of the carrier of V
W * x is right_complementable Element of the carrier of V
the lmult of V . (W,x) is right_complementable Element of the carrier of V
[W,x] is set
{W,x} is non empty set
{{W,x},{W}} is non empty set
the lmult of V . [W,x] is set
y is right_complementable Element of the carrier of V
W * y is right_complementable Element of the carrier of V
the lmult of V . (W,y) is right_complementable Element of the carrier of V
[W,y] is set
{W,y} is non empty set
{{W,y},{W}} is non empty set
the lmult of V . [W,y] is set
x + y is right_complementable Element of the carrier of V
the addF of V . (x,y) is right_complementable Element of the carrier of V
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of V . [x,y] is set
W * (x + y) is right_complementable Element of the carrier of V
the lmult of V . (W,(x + y)) is right_complementable Element of the carrier of V
[W,(x + y)] is set
{W,(x + y)} is non empty set
{{W,(x + y)},{W}} is non empty set
the lmult of V . [W,(x + y)] is set
(W * x) + (W * y) is right_complementable Element of the carrier of V
the addF of V . ((W * x),(W * y)) is right_complementable Element of the carrier of V
[(W * x),(W * y)] is set
{(W * x),(W * y)} is non empty set
{(W * x)} is non empty set
{{(W * x),(W * y)},{(W * x)}} is non empty set
the addF of V . [(W * x),(W * y)] is set
W is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of GF
W + W is right_complementable Element of the carrier of GF
the addF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the addF of GF . (W,W) is right_complementable Element of the carrier of GF
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the addF of GF . [W,W] is set
c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
(W + W) * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . ((W + W),c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(W + W),c₁₆] is set
{(W + W),c₁₆} is non empty set
{(W + W)} is non empty set
{{(W + W),c₁₆},{(W + W)}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [(W + W),c₁₆] is set
W * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (W,c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,c₁₆] is set
{W,c₁₆} is non empty set
{{W,c₁₆},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,c₁₆] is set
W * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (W,c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,c₁₆] is set
{W,c₁₆} is non empty set
{W} is non empty set
{{W,c₁₆},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,c₁₆] is set
(W * c₁₆) + (W * c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
the addF of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# W,u1,B,x #), the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the addF of VectSpStr(# W,u1,B,x #) . ((W * c₁₆),(W * c₁₆)) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(W * c₁₆),(W * c₁₆)] is set
{(W * c₁₆),(W * c₁₆)} is non empty set
{(W * c₁₆)} is non empty set
{{(W * c₁₆),(W * c₁₆)},{(W * c₁₆)}} is non empty set
the addF of VectSpStr(# W,u1,B,x #) . [(W * c₁₆),(W * c₁₆)] is set
y is right_complementable Element of the carrier of V
x is Element of the carrier of VectSpStr(# W,u1,B,x #)
y is right_complementable Element of the carrier of GF
[y,x] is Element of [: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):]
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
dom x is set
y * x is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (y,x) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[y,x] is set
the lmult of VectSpStr(# W,u1,B,x #) . [y,x] is set
y * y is right_complementable Element of the carrier of V
the lmult of V . (y,y) is right_complementable Element of the carrier of V
[y,y] is set
{y,y} is non empty set
{{y,y},{y}} is non empty set
the lmult of V . [y,y] is set
x is right_complementable Element of the carrier of V
W * x is right_complementable Element of the carrier of V
the lmult of V . (W,x) is right_complementable Element of the carrier of V
[W,x] is set
{W,x} is non empty set
{{W,x},{W}} is non empty set
the lmult of V . [W,x] is set
W * x is right_complementable Element of the carrier of V
the lmult of V . (W,x) is right_complementable Element of the carrier of V
[W,x] is set
{W,x} is non empty set
{{W,x},{W}} is non empty set
the lmult of V . [W,x] is set
W + W is right_complementable Element of the carrier of GF
(W + W) * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . ((W + W),c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(W + W),c₁₆] is set
{(W + W),c₁₆} is non empty set
{(W + W)} is non empty set
{{(W + W),c₁₆},{(W + W)}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [(W + W),c₁₆] is set
(W + W) * x is right_complementable Element of the carrier of V
the lmult of V . ((W + W),x) is right_complementable Element of the carrier of V
[(W + W),x] is set
{(W + W),x} is non empty set
{{(W + W),x},{(W + W)}} is non empty set
the lmult of V . [(W + W),x] is set
(W * x) + (W * x) is right_complementable Element of the carrier of V
the addF of V . ((W * x),(W * x)) is right_complementable Element of the carrier of V
[(W * x),(W * x)] is set
{(W * x),(W * x)} is non empty set
{(W * x)} is non empty set
{{(W * x),(W * x)},{(W * x)}} is non empty set
the addF of V . [(W * x),(W * x)] is set
W is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of GF
W * W is right_complementable Element of the carrier of GF
the multF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the multF of GF . (W,W) is right_complementable Element of the carrier of GF
[W,W] is set
{W,W} is non empty set
{W} is non empty set
{{W,W},{W}} is non empty set
the multF of GF . [W,W] is set
c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
(W * W) * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . ((W * W),c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(W * W),c₁₆] is set
{(W * W),c₁₆} is non empty set
{(W * W)} is non empty set
{{(W * W),c₁₆},{(W * W)}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [(W * W),c₁₆] is set
W * c₁₆ is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (W,c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,c₁₆] is set
{W,c₁₆} is non empty set
{W} is non empty set
{{W,c₁₆},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,c₁₆] is set
W * (W * c₁₆) is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (W,(W * c₁₆)) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[W,(W * c₁₆)] is set
{W,(W * c₁₆)} is non empty set
{{W,(W * c₁₆)},{W}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [W,(W * c₁₆)] is set
y is right_complementable Element of the carrier of V
x is Element of the carrier of VectSpStr(# W,u1,B,x #)
y is right_complementable Element of the carrier of GF
[y,x] is Element of [: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):]
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
dom x is set
y * x is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (y,x) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[y,x] is set
the lmult of VectSpStr(# W,u1,B,x #) . [y,x] is set
y * y is right_complementable Element of the carrier of V
the lmult of V . (y,y) is right_complementable Element of the carrier of V
[y,y] is set
{y,y} is non empty set
{{y,y},{y}} is non empty set
the lmult of V . [y,y] is set
x is right_complementable Element of the carrier of V
W * x is right_complementable Element of the carrier of V
the lmult of V . (W,x) is right_complementable Element of the carrier of V
[W,x] is set
{W,x} is non empty set
{{W,x},{W}} is non empty set
the lmult of V . [W,x] is set
(W * W) * x is right_complementable Element of the carrier of V
the lmult of V . ((W * W),x) is right_complementable Element of the carrier of V
[(W * W),x] is set
{(W * W),x} is non empty set
{{(W * W),x},{(W * W)}} is non empty set
the lmult of V . [(W * W),x] is set
W * (W * x) is right_complementable Element of the carrier of V
the lmult of V . (W,(W * x)) is right_complementable Element of the carrier of V
[W,(W * x)] is set
{W,(W * x)} is non empty set
{{W,(W * x)},{W}} is non empty set
the lmult of V . [W,(W * x)] is set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
W is Element of the carrier of VectSpStr(# W,u1,B,x #)
(1. GF) * W is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):]
[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):], the carrier of VectSpStr(# W,u1,B,x #):] is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . ((1. GF),W) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[(1. GF),W] is set
{(1. GF),W} is non empty set
{(1. GF)} is non empty set
{{(1. GF),W},{(1. GF)}} is non empty set
the lmult of VectSpStr(# W,u1,B,x #) . [(1. GF),W] is set
y is right_complementable Element of the carrier of V
x is Element of the carrier of VectSpStr(# W,u1,B,x #)
c₁₆ is right_complementable Element of the carrier of GF
[c₁₆,x] is Element of [: the carrier of GF, the carrier of VectSpStr(# W,u1,B,x #):]
{c₁₆,x} is non empty set
{c₁₆} is non empty set
{{c₁₆,x},{c₁₆}} is non empty set
dom x is set
c₁₆ * x is Element of the carrier of VectSpStr(# W,u1,B,x #)
the lmult of VectSpStr(# W,u1,B,x #) . (c₁₆,x) is Element of the carrier of VectSpStr(# W,u1,B,x #)
[c₁₆,x] is set
the lmult of VectSpStr(# W,u1,B,x #) . [c₁₆,x] is set
c₁₆ * y is right_complementable Element of the carrier of V
the lmult of V . (c₁₆,y) is right_complementable Element of the carrier of V
[c₁₆,y] is set
{c₁₆,y} is non empty set
{{c₁₆,y},{c₁₆}} is non empty set
the lmult of V . [c₁₆,y] is set
1_ GF is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
(1_ GF) * W is right_complementable Element of the carrier of V
the lmult of V . ((1_ GF),W) is right_complementable Element of the carrier of V
[(1_ GF),W] is set
{(1_ GF),W} is non empty set
{(1_ GF)} is non empty set
{{(1_ GF),W},{(1_ GF)}} is non empty set
the lmult of V . [(1_ GF),W] is set
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
0. W is V49(W) right_complementable Element of the carrier of W
the carrier of W is non empty set
the ZeroF of W is right_complementable Element of the carrier of W
W is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of W is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of W is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty strict VectSpStr over GF
the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty set
W is right_complementable Element of the carrier of GF
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [B,C] is set
W * (B + C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,(B + C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,(B + C)] is set
{W,(B + C)} is non empty set
{W} is non empty set
{{W,(B + C)},{W}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,(B + C)] is set
W * B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,B) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,B] is set
{W,B} is non empty set
{{W,B},{W}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,B] is set
W * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,C] is set
(W * B) + (W * C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((W * B),(W * C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(W * B),(W * C)] is set
{(W * B),(W * C)} is non empty set
{(W * B)} is non empty set
{{(W * B),(W * C)},{(W * B)}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(W * B),(W * C)] is set
C is right_complementable Element of the carrier of V
c₈ is right_complementable Element of the carrier of V
C + c₈ is right_complementable Element of the carrier of V
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
W * (C + c₈) is right_complementable Element of the carrier of V
the lmult of V . (W,(C + c₈)) is right_complementable Element of the carrier of V
[W,(C + c₈)] is set
{W,(C + c₈)} is non empty set
{{W,(C + c₈)},{W}} is non empty set
the lmult of V . [W,(C + c₈)] is set
W * C is right_complementable Element of the carrier of V
the lmult of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the lmult of V . [W,C] is set
W * c₈ is right_complementable Element of the carrier of V
the lmult of V . (W,c₈) is right_complementable Element of the carrier of V
[W,c₈] is set
{W,c₈} is non empty set
{{W,c₈},{W}} is non empty set
the lmult of V . [W,c₈] is set
(W * C) + (W * c₈) is right_complementable Element of the carrier of V
the addF of V . ((W * C),(W * c₈)) is right_complementable Element of the carrier of V
[(W * C),(W * c₈)] is set
{(W * C),(W * c₈)} is non empty set
{(W * C)} is non empty set
{{(W * C),(W * c₈)},{(W * C)}} is non empty set
the addF of V . [(W * C),(W * c₈)] is set
the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty set
W is right_complementable Element of the carrier of GF
B is right_complementable Element of the carrier of GF
W + B is right_complementable Element of the carrier of GF
the addF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the addF of GF . (W,B) is right_complementable Element of the carrier of GF
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the addF of GF . [W,B] is set
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
(W + B) * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((W + B),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(W + B),C] is set
{(W + B),C} is non empty set
{(W + B)} is non empty set
{{(W + B),C},{(W + B)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(W + B),C] is set
W * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,C] is set
B * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [B,C] is set
(W * C) + (B * C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((W * C),(B * C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(W * C),(B * C)] is set
{(W * C),(B * C)} is non empty set
{(W * C)} is non empty set
{{(W * C),(B * C)},{(W * C)}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(W * C),(B * C)] is set
W + B is right_complementable Element of the carrier of GF
(W + B) * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((W + B),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(W + B),C] is set
{(W + B),C} is non empty set
{(W + B)} is non empty set
{{(W + B),C},{(W + B)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(W + B),C] is set
C is right_complementable Element of the carrier of V
(W + B) * C is right_complementable Element of the carrier of V
the lmult of V . ((W + B),C) is right_complementable Element of the carrier of V
[(W + B),C] is set
{(W + B),C} is non empty set
{{(W + B),C},{(W + B)}} is non empty set
the lmult of V . [(W + B),C] is set
W * C is right_complementable Element of the carrier of V
the lmult of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the lmult of V . [W,C] is set
B * C is right_complementable Element of the carrier of V
the lmult of V . (B,C) is right_complementable Element of the carrier of V
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the lmult of V . [B,C] is set
(W * C) + (B * C) is right_complementable Element of the carrier of V
the addF of V . ((W * C),(B * C)) is right_complementable Element of the carrier of V
[(W * C),(B * C)] is set
{(W * C),(B * C)} is non empty set
{(W * C)} is non empty set
{{(W * C),(B * C)},{(W * C)}} is non empty set
the addF of V . [(W * C),(B * C)] is set
the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty set
W is right_complementable Element of the carrier of GF
B is right_complementable Element of the carrier of GF
W * B is right_complementable Element of the carrier of GF
the multF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the multF of GF . (W,B) is right_complementable Element of the carrier of GF
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the multF of GF . [W,B] is set
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
(W * B) * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((W * B),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(W * B),C] is set
{(W * B),C} is non empty set
{(W * B)} is non empty set
{{(W * B),C},{(W * B)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(W * B),C] is set
B * C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [B,C] is set
W * (B * C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,(B * C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,(B * C)] is set
{W,(B * C)} is non empty set
{{W,(B * C)},{W}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,(B * C)] is set
C is right_complementable Element of the carrier of V
(W * B) * C is right_complementable Element of the carrier of V
the lmult of V . ((W * B),C) is right_complementable Element of the carrier of V
[(W * B),C] is set
{(W * B),C} is non empty set
{{(W * B),C},{(W * B)}} is non empty set
the lmult of V . [(W * B),C] is set
B * C is right_complementable Element of the carrier of V
the lmult of V . (B,C) is right_complementable Element of the carrier of V
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the lmult of V . [B,C] is set
W * (B * C) is right_complementable Element of the carrier of V
the lmult of V . (W,(B * C)) is right_complementable Element of the carrier of V
[W,(B * C)] is set
{W,(B * C)} is non empty set
{{W,(B * C)},{W}} is non empty set
the lmult of V . [W,(B * C)] is set
the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
(1. GF) * W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((1. GF),W) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(1. GF),W] is set
{(1. GF),W} is non empty set
{(1. GF)} is non empty set
{{(1. GF),W},{(1. GF)}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(1. GF),W] is set
1_ GF is right_complementable Element of the carrier of GF
B is right_complementable Element of the carrier of V
(1_ GF) * B is right_complementable Element of the carrier of V
the lmult of V . ((1_ GF),B) is right_complementable Element of the carrier of V
[(1_ GF),B] is set
{(1_ GF),B} is non empty set
{(1_ GF)} is non empty set
{{(1_ GF),B},{(1_ GF)}} is non empty set
the lmult of V . [(1_ GF),B] is set
the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty set
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
C is right_complementable Element of the carrier of V
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
c₈ is right_complementable Element of the carrier of V
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [B,C] is set
C + c₈ is right_complementable Element of the carrier of V
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
W is right_complementable Element of the carrier of GF
W * B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,B) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the lmult of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,B] is set
W * C is right_complementable Element of the carrier of V
the lmult of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the lmult of V . [W,C] is set
W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
W + B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,B) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,B] is set
B + W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (B,W) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[B,W] is set
{B,W} is non empty set
{B} is non empty set
{{B,W},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [B,W] is set
C is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
C + C is right_complementable Element of the carrier of V
the addF of V . (C,C) is right_complementable Element of the carrier of V
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the addF of V . [C,C] is set
W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
W + B is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Relation-like Function-like V18([: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):]
[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
[:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is Relation-like non empty set
bool [:[: the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #), the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):], the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #):] is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,B) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,B] is set
(W + B) + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . ((W + B),C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[(W + B),C] is set
{(W + B),C} is non empty set
{(W + B)} is non empty set
{{(W + B),C},{(W + B)}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [(W + B),C] is set
C is right_complementable Element of the carrier of V
c₈ is right_complementable Element of the carrier of V
C + c₈ is right_complementable Element of the carrier of V
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
x is right_complementable Element of the carrier of V
(C + c₈) + x is right_complementable Element of the carrier of V
the addF of V . ((C + c₈),x) is right_complementable Element of the carrier of V
[(C + c₈),x] is set
{(C + c₈),x} is non empty set
{(C + c₈)} is non empty set
{{(C + c₈),x},{(C + c₈)}} is non empty set
the addF of V . [(C + c₈),x] is set
c₈ + x is right_complementable Element of the carrier of V
the addF of V . (c₈,x) is right_complementable Element of the carrier of V
[c₈,x] is set
{c₈,x} is non empty set
{c₈} is non empty set
{{c₈,x},{c₈}} is non empty set
the addF of V . [c₈,x] is set
C + (c₈ + x) is right_complementable Element of the carrier of V
the addF of V . (C,(c₈ + x)) is right_complementable Element of the carrier of V
[C,(c₈ + x)] is set
{C,(c₈ + x)} is non empty set
{{C,(c₈ + x)},{C}} is non empty set
the addF of V . [C,(c₈ + x)] is set
B + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (B,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [B,C] is set
W + (B + C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,(B + C)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,(B + C)] is set
{W,(B + C)} is non empty set
{{W,(B + C)},{W}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,(B + C)] is set
W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is V49( VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the ZeroF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
W + (0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,(0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #))) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,(0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #))] is set
{W,(0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #))} is non empty set
{W} is non empty set
{{W,(0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #))},{W}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,(0. VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #))] is set
B is right_complementable Element of the carrier of V
0. V is V49(V) right_complementable Element of the carrier of V
B + (0. V) is right_complementable Element of the carrier of V
the addF of V . (B,(0. V)) is right_complementable Element of the carrier of V
[B,(0. V)] is set
{B,(0. V)} is non empty set
{B} is non empty set
{{B,(0. V)},{B}} is non empty set
the addF of V . [B,(0. V)] is set
W is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
B is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
B + C is right_complementable Element of the carrier of V
the addF of V . (B,C) is right_complementable Element of the carrier of V
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the addF of V . [B,C] is set
C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
W + C is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . (W,C) is Element of the carrier of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #)
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) . [W,C] is set
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the lmult of W is Relation-like Function-like V18([: the carrier of GF, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of GF, the carrier of W:], the carrier of W:]
the carrier of W is non empty set
[: the carrier of GF, the carrier of W:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of W:], the carrier of W:] is non empty set
the lmult of V | [: the carrier of GF, the carrier of W:] is Relation-like Function-like set
0. W is V49(W) right_complementable Element of the carrier of W
the ZeroF of W is right_complementable Element of the carrier of W
0. V is V49(V) right_complementable Element of the carrier of V
the addF of W is Relation-like Function-like V18([: the carrier of W, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of W, the carrier of W:], the carrier of W:]
[: the carrier of W, the carrier of W:] is Relation-like non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of W, the carrier of W:], the carrier of W:] is non empty set
the addF of V || the carrier of W is Relation-like Function-like set
the addF of V | [: the carrier of W, the carrier of W:] is Relation-like Function-like set
GF is set
V is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V
(V,u) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (V,u)
0. u is V49(u) right_complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is right_complementable Element of the carrier of u
the carrier of (V,u) is non empty set
{(0. u)} is non empty Element of bool the carrier of u
bool the carrier of u is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,u) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,u)
the carrier of (GF,u) is non empty set
the carrier of u is non empty set
0. u is V49(u) right_complementable Element of the carrier of u
the ZeroF of u is right_complementable Element of the carrier of u
{(0. u)} is non empty Element of bool the carrier of u
bool the carrier of u is non empty set
the carrier of (GF,V) is non empty set
the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,u) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,u)
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,W) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,W)
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,u) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,u)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,u) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,u)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,u) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,u)
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,W) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,W)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of V is non empty set
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty strict VectSpStr over GF
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
bool the carrier of V is non empty set
C is set
C is set
C is Element of bool the carrier of V
c₈ is set
x is right_complementable Element of the carrier of V
u + x is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,x) is right_complementable Element of the carrier of V
[u,x] is set
{u,x} is non empty set
{u} is non empty set
{{u,x},{u}} is non empty set
the addF of V . [u,x] is set
c₈ is set
x is right_complementable Element of the carrier of V
u + x is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,x) is right_complementable Element of the carrier of V
[u,x] is set
{u,x} is non empty set
{u} is non empty set
{{u,x},{u}} is non empty set
the addF of V . [u,x] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,(0. V),u) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((0. V) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
the carrier of u is non empty set
B is set
C is right_complementable Element of the carrier of V
(0. V) + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((0. V),C) is right_complementable Element of the carrier of V
[(0. V),C] is set
{(0. V),C} is non empty set
{(0. V)} is non empty set
{{(0. V),C},{(0. V)}} is non empty set
the addF of V . [(0. V),C] is set
B is set
C is right_complementable Element of the carrier of V
(0. V) + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((0. V),C) is right_complementable Element of the carrier of V
[(0. V),C] is set
{(0. V),C} is non empty set
{(0. V)} is non empty set
{{(0. V),C},{(0. V)}} is non empty set
the addF of V . [(0. V),C] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is Element of bool the carrier of V
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(GF,V,(0. V),u) is Element of bool the carrier of V
{ ((0. V) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
GF is set
V is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over V
the carrier of u is non empty set
W is right_complementable Element of the carrier of u
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (V,u)
(V,u,W,B) is Element of bool the carrier of u
bool the carrier of u is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of u : b₁ in B } is set
C is right_complementable Element of the carrier of u
W + C is right_complementable Element of the carrier of u
the addF of u is Relation-like Function-like V18([: the carrier of u, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of u, the carrier of u:], the carrier of u:]
[: the carrier of u, the carrier of u:] is Relation-like non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of u . (W,C) is right_complementable Element of the carrier of u
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of u . [W,C] is set
C is right_complementable Element of the carrier of u
W + C is right_complementable Element of the carrier of u
the addF of u is Relation-like Function-like V18([: the carrier of u, the carrier of u:], the carrier of u) Element of bool [:[: the carrier of u, the carrier of u:], the carrier of u:]
[: the carrier of u, the carrier of u:] is Relation-like non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is Relation-like non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of u . (W,C) is right_complementable Element of the carrier of u
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of u . [W,C] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
B is right_complementable Element of the carrier of V
u + B is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,B) is right_complementable Element of the carrier of V
[u,B] is set
{u,B} is non empty set
{u} is non empty set
{{u,B},{u}} is non empty set
the addF of V . [u,B] is set
- B is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
u + (- u) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(- u)) is right_complementable Element of the carrier of V
[u,(- u)] is set
{u,(- u)} is non empty set
{u} is non empty set
{{u,(- u)},{u}} is non empty set
the addF of V . [u,(- u)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
u + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(0. V)) is right_complementable Element of the carrier of V
[u,(0. V)] is set
{u,(0. V)} is non empty set
{u} is non empty set
{{u,(0. V)},{u}} is non empty set
the addF of V . [u,(0. V)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,(0. V),u) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((0. V) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
the carrier of u is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
u is right_complementable Element of the carrier of V
(GF,V,u,(GF,V)) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in (GF,V) } is set
{u} is non empty Element of bool the carrier of V
W is set
B is right_complementable Element of the carrier of V
u + B is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,B) is right_complementable Element of the carrier of V
[u,B] is set
{u,B} is non empty set
{u} is non empty set
{{u,B},{u}} is non empty set
the addF of V . [u,B] is set
the carrier of (GF,V) is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty Element of bool the carrier of V
W is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
u + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(0. V)) is right_complementable Element of the carrier of V
[u,(0. V)] is set
{u,(0. V)} is non empty set
{u} is non empty set
{{u,(0. V)},{u}} is non empty set
the addF of V . [u,(0. V)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
the carrier of W is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
u + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(0. V)) is right_complementable Element of the carrier of V
[u,(0. V)] is set
{u,(0. V)} is non empty set
{u} is non empty set
{{u,(0. V)},{u}} is non empty set
the addF of V . [u,(0. V)] is set
B is set
C is right_complementable Element of the carrier of V
u + C is right_complementable Element of the carrier of V
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
B is set
C is right_complementable Element of the carrier of W
C is right_complementable Element of the carrier of W
C - C is right_complementable Element of the carrier of W
- C is right_complementable Element of the carrier of W
C + (- C) is right_complementable Element of the carrier of W
the addF of W is Relation-like Function-like V18([: the carrier of W, the carrier of W:], the carrier of W) Element of bool [:[: the carrier of W, the carrier of W:], the carrier of W:]
[: the carrier of W, the carrier of W:] is Relation-like non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is Relation-like non empty set
bool [:[: the carrier of W, the carrier of W:], the carrier of W:] is non empty set
the addF of W . (C,(- C)) is right_complementable Element of the carrier of W
[C,(- C)] is set
{C,(- C)} is non empty set
{C} is non empty set
{{C,(- C)},{C}} is non empty set
the addF of W . [C,(- C)] is set
C + (C - C) is right_complementable Element of the carrier of W
the addF of W . (C,(C - C)) is right_complementable Element of the carrier of W
[C,(C - C)] is set
{C,(C - C)} is non empty set
{C} is non empty set
{{C,(C - C)},{C}} is non empty set
the addF of W . [C,(C - C)] is set
C + (- C) is right_complementable Element of the carrier of W
the addF of W . (C,(- C)) is right_complementable Element of the carrier of W
[C,(- C)] is set
{C,(- C)} is non empty set
{{C,(- C)},{C}} is non empty set
the addF of W . [C,(- C)] is set
C + (C + (- C)) is right_complementable Element of the carrier of W
the addF of W . (C,(C + (- C))) is right_complementable Element of the carrier of W
[C,(C + (- C))] is set
{C,(C + (- C))} is non empty set
{{C,(C + (- C))},{C}} is non empty set
the addF of W . [C,(C + (- C))] is set
0. W is V49(W) right_complementable Element of the carrier of W
the ZeroF of W is right_complementable Element of the carrier of W
C + (0. W) is right_complementable Element of the carrier of W
the addF of W . (C,(0. W)) is right_complementable Element of the carrier of W
[C,(0. W)] is set
{C,(0. W)} is non empty set
{{C,(0. W)},{C}} is non empty set
the addF of W . [C,(0. W)] is set
c₈ is right_complementable Element of the carrier of V
x is right_complementable Element of the carrier of V
c₈ - x is right_complementable Element of the carrier of V
- x is right_complementable Element of the carrier of V
c₈ + (- x) is right_complementable Element of the carrier of V
the addF of V . (c₈,(- x)) is right_complementable Element of the carrier of V
[c₈,(- x)] is set
{c₈,(- x)} is non empty set
{c₈} is non empty set
{{c₈,(- x)},{c₈}} is non empty set
the addF of V . [c₈,(- x)] is set
x + (c₈ - x) is right_complementable Element of the carrier of V
the addF of V . (x,(c₈ - x)) is right_complementable Element of the carrier of V
[x,(c₈ - x)] is set
{x,(c₈ - x)} is non empty set
{x} is non empty set
{{x,(c₈ - x)},{x}} is non empty set
the addF of V . [x,(c₈ - x)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty strict VectSpStr over GF
u is right_complementable Element of the carrier of V
(GF,V,u,(GF,V)) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in (GF,V) } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
the carrier of W is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
B is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
C is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over B
the carrier of C is non empty set
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
u is right_complementable Element of the carrier of V
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
the carrier of W is non empty set
C is right_complementable Element of the carrier of C
c₈ is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (B,C)
(B,C,C,c₈) is Element of bool the carrier of C
bool the carrier of C is non empty set
{ (C + b₁) where b₁ is right_complementable Element of the carrier of C : b₁ in c₈ } is set
the carrier of c₈ is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty set
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,(u * W),B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((u * W) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
the carrier of B is non empty set
GF is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty non trivial set
0. GF is V49(GF) right_complementable Element of the carrier of GF
the ZeroF of GF is right_complementable Element of the carrier of GF
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,(u * W),B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((u * W) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
the carrier of B is non empty set
1_ GF is right_complementable Element of the carrier of GF
1. GF is V49(GF) right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
(1_ GF) * W is right_complementable Element of the carrier of V
the lmult of V . ((1_ GF),W) is right_complementable Element of the carrier of V
[(1_ GF),W] is set
{(1_ GF),W} is non empty set
{(1_ GF)} is non empty set
{{(1_ GF),W},{(1_ GF)}} is non empty set
the lmult of V . [(1_ GF),W] is set
u " is right_complementable Element of the carrier of GF
(u ") * u is right_complementable Element of the carrier of GF
the multF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the multF of GF . ((u "),u) is right_complementable Element of the carrier of GF
[(u "),u] is set
{(u "),u} is non empty set
{(u ")} is non empty set
{{(u "),u},{(u ")}} is non empty set
the multF of GF . [(u "),u] is set
((u ") * u) * W is right_complementable Element of the carrier of V
the lmult of V . (((u ") * u),W) is right_complementable Element of the carrier of V
[((u ") * u),W] is set
{((u ") * u),W} is non empty set
{((u ") * u)} is non empty set
{{((u ") * u),W},{((u ") * u)}} is non empty set
the lmult of V . [((u ") * u),W] is set
(u ") * (u * W) is right_complementable Element of the carrier of V
the lmult of V . ((u "),(u * W)) is right_complementable Element of the carrier of V
[(u "),(u * W)] is set
{(u "),(u * W)} is non empty set
{{(u "),(u * W)},{(u ")}} is non empty set
the lmult of V . [(u "),(u * W)] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(u * W) + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((u * W),(0. V)) is right_complementable Element of the carrier of V
[(u * W),(0. V)] is set
{(u * W),(0. V)} is non empty set
{(u * W)} is non empty set
{{(u * W),(0. V)},{(u * W)}} is non empty set
the addF of V . [(u * W),(0. V)] is set
GF is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,(- u),W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((- u) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
the carrier of W is non empty set
1_ GF is right_complementable Element of the carrier of GF
the carrier of GF is non empty non trivial set
1. GF is V49(GF) right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
- (1_ GF) is right_complementable Element of the carrier of GF
0. GF is V49(GF) right_complementable Element of the carrier of GF
the ZeroF of GF is right_complementable Element of the carrier of GF
(- (1_ GF)) * u is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((- (1_ GF)),u) is right_complementable Element of the carrier of V
[(- (1_ GF)),u] is set
{(- (1_ GF)),u} is non empty set
{(- (1_ GF))} is non empty set
{{(- (1_ GF)),u},{(- (1_ GF))}} is non empty set
the lmult of V . [(- (1_ GF)),u] is set
(GF,V,((- (1_ GF)) * u),W) is Element of bool the carrier of V
{ (((- (1_ GF)) * u) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
W + u is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,u) is right_complementable Element of the carrier of V
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the addF of V . [W,u] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,(W + u),B) is Element of bool the carrier of V
{ ((W + u) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is set
C is right_complementable Element of the carrier of V
W + C is right_complementable Element of the carrier of V
the addF of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the addF of V . [W,C] is set
C - u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
C + (- u) is right_complementable Element of the carrier of V
the addF of V . (C,(- u)) is right_complementable Element of the carrier of V
[C,(- u)] is set
{C,(- u)} is non empty set
{C} is non empty set
{{C,(- u)},{C}} is non empty set
the addF of V . [C,(- u)] is set
(W + u) + (C - u) is right_complementable Element of the carrier of V
the addF of V . ((W + u),(C - u)) is right_complementable Element of the carrier of V
[(W + u),(C - u)] is set
{(W + u),(C - u)} is non empty set
{(W + u)} is non empty set
{{(W + u),(C - u)},{(W + u)}} is non empty set
the addF of V . [(W + u),(C - u)] is set
u + (C - u) is right_complementable Element of the carrier of V
the addF of V . (u,(C - u)) is right_complementable Element of the carrier of V
[u,(C - u)] is set
{u,(C - u)} is non empty set
{u} is non empty set
{{u,(C - u)},{u}} is non empty set
the addF of V . [u,(C - u)] is set
W + (u + (C - u)) is right_complementable Element of the carrier of V
the addF of V . (W,(u + (C - u))) is right_complementable Element of the carrier of V
[W,(u + (C - u))] is set
{W,(u + (C - u))} is non empty set
{{W,(u + (C - u))},{W}} is non empty set
the addF of V . [W,(u + (C - u))] is set
C + u is right_complementable Element of the carrier of V
the addF of V . (C,u) is right_complementable Element of the carrier of V
[C,u] is set
{C,u} is non empty set
{{C,u},{C}} is non empty set
the addF of V . [C,u] is set
(C + u) - u is right_complementable Element of the carrier of V
(C + u) + (- u) is right_complementable Element of the carrier of V
the addF of V . ((C + u),(- u)) is right_complementable Element of the carrier of V
[(C + u),(- u)] is set
{(C + u),(- u)} is non empty set
{(C + u)} is non empty set
{{(C + u),(- u)},{(C + u)}} is non empty set
the addF of V . [(C + u),(- u)] is set
W + ((C + u) - u) is right_complementable Element of the carrier of V
the addF of V . (W,((C + u) - u)) is right_complementable Element of the carrier of V
[W,((C + u) - u)] is set
{W,((C + u) - u)} is non empty set
{{W,((C + u) - u)},{W}} is non empty set
the addF of V . [W,((C + u) - u)] is set
u - u is right_complementable Element of the carrier of V
u + (- u) is right_complementable Element of the carrier of V
the addF of V . (u,(- u)) is right_complementable Element of the carrier of V
[u,(- u)] is set
{u,(- u)} is non empty set
{{u,(- u)},{u}} is non empty set
the addF of V . [u,(- u)] is set
C + (u - u) is right_complementable Element of the carrier of V
the addF of V . (C,(u - u)) is right_complementable Element of the carrier of V
[C,(u - u)] is set
{C,(u - u)} is non empty set
{{C,(u - u)},{C}} is non empty set
the addF of V . [C,(u - u)] is set
W + (C + (u - u)) is right_complementable Element of the carrier of V
the addF of V . (W,(C + (u - u))) is right_complementable Element of the carrier of V
[W,(C + (u - u))] is set
{W,(C + (u - u))} is non empty set
{{W,(C + (u - u))},{W}} is non empty set
the addF of V . [W,(C + (u - u))] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
C + (0. V) is right_complementable Element of the carrier of V
the addF of V . (C,(0. V)) is right_complementable Element of the carrier of V
[C,(0. V)] is set
{C,(0. V)} is non empty set
{{C,(0. V)},{C}} is non empty set
the addF of V . [C,(0. V)] is set
W + (C + (0. V)) is right_complementable Element of the carrier of V
the addF of V . (W,(C + (0. V))) is right_complementable Element of the carrier of V
[W,(C + (0. V))] is set
{W,(C + (0. V))} is non empty set
{{W,(C + (0. V))},{W}} is non empty set
the addF of V . [W,(C + (0. V))] is set
C is set
C is right_complementable Element of the carrier of V
(W + u) + C is right_complementable Element of the carrier of V
the addF of V . ((W + u),C) is right_complementable Element of the carrier of V
[(W + u),C] is set
{(W + u),C} is non empty set
{(W + u)} is non empty set
{{(W + u),C},{(W + u)}} is non empty set
the addF of V . [(W + u),C] is set
u + C is right_complementable Element of the carrier of V
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{u} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
W + (u + C) is right_complementable Element of the carrier of V
the addF of V . (W,(u + C)) is right_complementable Element of the carrier of V
[W,(u + C)] is set
{W,(u + C)} is non empty set
{{W,(u + C)},{W}} is non empty set
the addF of V . [W,(u + C)] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
W + (0. V) is right_complementable Element of the carrier of V
the addF of V . (W,(0. V)) is right_complementable Element of the carrier of V
[W,(0. V)] is set
{W,(0. V)} is non empty set
{{W,(0. V)},{W}} is non empty set
the addF of V . [W,(0. V)] is set
C is right_complementable Element of the carrier of V
(W + u) + C is right_complementable Element of the carrier of V
the addF of V . ((W + u),C) is right_complementable Element of the carrier of V
[(W + u),C] is set
{(W + u),C} is non empty set
{(W + u)} is non empty set
{{(W + u),C},{(W + u)}} is non empty set
the addF of V . [(W + u),C] is set
u + C is right_complementable Element of the carrier of V
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{u} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
W + (u + C) is right_complementable Element of the carrier of V
the addF of V . (W,(u + C)) is right_complementable Element of the carrier of V
[W,(u + C)] is set
{W,(u + C)} is non empty set
{{W,(u + C)},{W}} is non empty set
the addF of V . [W,(u + C)] is set
- C is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
W - u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
W + (- u) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,(- u)) is right_complementable Element of the carrier of V
[W,(- u)] is set
{W,(- u)} is non empty set
{W} is non empty set
{{W,(- u)},{W}} is non empty set
the addF of V . [W,(- u)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,(W - u),B) is Element of bool the carrier of V
{ ((W - u) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
- (- u) is right_complementable Element of the carrier of V
W + (- u) is right_complementable Element of the carrier of V
(GF,V,(W + (- u)),B) is Element of bool the carrier of V
{ ((W + (- u)) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,u,B) is Element of bool the carrier of V
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
W + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of V . [W,C] is set
C is set
c₈ is right_complementable Element of the carrier of V
W + c₈ is right_complementable Element of the carrier of V
the addF of V . (W,c₈) is right_complementable Element of the carrier of V
[W,c₈] is set
{W,c₈} is non empty set
{{W,c₈},{W}} is non empty set
the addF of V . [W,c₈] is set
u - C is right_complementable Element of the carrier of V
- C is right_complementable Element of the carrier of V
u + (- C) is right_complementable Element of the carrier of V
the addF of V . (u,(- C)) is right_complementable Element of the carrier of V
[u,(- C)] is set
{u,(- C)} is non empty set
{u} is non empty set
{{u,(- C)},{u}} is non empty set
the addF of V . [u,(- C)] is set
C - C is right_complementable Element of the carrier of V
C + (- C) is right_complementable Element of the carrier of V
the addF of V . (C,(- C)) is right_complementable Element of the carrier of V
[C,(- C)] is set
{C,(- C)} is non empty set
{C} is non empty set
{{C,(- C)},{C}} is non empty set
the addF of V . [C,(- C)] is set
W + (C - C) is right_complementable Element of the carrier of V
the addF of V . (W,(C - C)) is right_complementable Element of the carrier of V
[W,(C - C)] is set
{W,(C - C)} is non empty set
{{W,(C - C)},{W}} is non empty set
the addF of V . [W,(C - C)] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
W + (0. V) is right_complementable Element of the carrier of V
the addF of V . (W,(0. V)) is right_complementable Element of the carrier of V
[W,(0. V)] is set
{W,(0. V)} is non empty set
{{W,(0. V)},{W}} is non empty set
the addF of V . [W,(0. V)] is set
c₈ + (- C) is right_complementable Element of the carrier of V
the addF of V . (c₈,(- C)) is right_complementable Element of the carrier of V
[c₈,(- C)] is set
{c₈,(- C)} is non empty set
{c₈} is non empty set
{{c₈,(- C)},{c₈}} is non empty set
the addF of V . [c₈,(- C)] is set
u + (c₈ + (- C)) is right_complementable Element of the carrier of V
the addF of V . (u,(c₈ + (- C))) is right_complementable Element of the carrier of V
[u,(c₈ + (- C))] is set
{u,(c₈ + (- C))} is non empty set
{{u,(c₈ + (- C))},{u}} is non empty set
the addF of V . [u,(c₈ + (- C))] is set
c₈ - C is right_complementable Element of the carrier of V
c₈ + (- C) is right_complementable Element of the carrier of V
u + (c₈ - C) is right_complementable Element of the carrier of V
the addF of V . (u,(c₈ - C)) is right_complementable Element of the carrier of V
[u,(c₈ - C)] is set
{u,(c₈ - C)} is non empty set
{{u,(c₈ - C)},{u}} is non empty set
the addF of V . [u,(c₈ - C)] is set
C is set
c₈ is right_complementable Element of the carrier of V
u + c₈ is right_complementable Element of the carrier of V
the addF of V . (u,c₈) is right_complementable Element of the carrier of V
[u,c₈] is set
{u,c₈} is non empty set
{u} is non empty set
{{u,c₈},{u}} is non empty set
the addF of V . [u,c₈] is set
C + c₈ is right_complementable Element of the carrier of V
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{C} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
W + (C + c₈) is right_complementable Element of the carrier of V
the addF of V . (W,(C + c₈)) is right_complementable Element of the carrier of V
[W,(C + c₈)] is set
{W,(C + c₈)} is non empty set
{{W,(C + c₈)},{W}} is non empty set
the addF of V . [W,(C + c₈)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is right_complementable Element of the carrier of V
C is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,C) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
(GF,V,B,C) is Element of bool the carrier of V
{ (B + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
(GF,V,u,C) is Element of bool the carrier of V
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
GF is non empty non degenerated non trivial right_complementable almost_left_invertible unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty non trivial set
1_ GF is right_complementable Element of the carrier of GF
1. GF is V49(GF) right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
u - (1_ GF) is right_complementable Element of the carrier of GF
- (1_ GF) is right_complementable Element of the carrier of GF
u + (- (1_ GF)) is right_complementable Element of the carrier of GF
the addF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the addF of GF . (u,(- (1_ GF))) is right_complementable Element of the carrier of GF
[u,(- (1_ GF))] is set
{u,(- (1_ GF))} is non empty set
{{u,(- (1_ GF))},{u}} is non empty set
the addF of GF . [u,(- (1_ GF))] is set
0. GF is V49(GF) right_complementable Element of the carrier of GF
the ZeroF of GF is right_complementable Element of the carrier of GF
C is right_complementable Element of the carrier of V
W + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of V . [W,C] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
C + (0. V) is right_complementable Element of the carrier of V
the addF of V . (C,(0. V)) is right_complementable Element of the carrier of V
[C,(0. V)] is set
{C,(0. V)} is non empty set
{C} is non empty set
{{C,(0. V)},{C}} is non empty set
the addF of V . [C,(0. V)] is set
W - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
W + (- W) is right_complementable Element of the carrier of V
the addF of V . (W,(- W)) is right_complementable Element of the carrier of V
[W,(- W)] is set
{W,(- W)} is non empty set
{{W,(- W)},{W}} is non empty set
the addF of V . [W,(- W)] is set
C + (W - W) is right_complementable Element of the carrier of V
the addF of V . (C,(W - W)) is right_complementable Element of the carrier of V
[C,(W - W)] is set
{C,(W - W)} is non empty set
{{C,(W - W)},{C}} is non empty set
the addF of V . [C,(W - W)] is set
(u * W) - W is right_complementable Element of the carrier of V
(u * W) + (- W) is right_complementable Element of the carrier of V
the addF of V . ((u * W),(- W)) is right_complementable Element of the carrier of V
[(u * W),(- W)] is set
{(u * W),(- W)} is non empty set
{(u * W)} is non empty set
{{(u * W),(- W)},{(u * W)}} is non empty set
the addF of V . [(u * W),(- W)] is set
(1_ GF) * W is right_complementable Element of the carrier of V
the lmult of V . ((1_ GF),W) is right_complementable Element of the carrier of V
[(1_ GF),W] is set
{(1_ GF),W} is non empty set
{(1_ GF)} is non empty set
{{(1_ GF),W},{(1_ GF)}} is non empty set
the lmult of V . [(1_ GF),W] is set
(u * W) - ((1_ GF) * W) is right_complementable Element of the carrier of V
- ((1_ GF) * W) is right_complementable Element of the carrier of V
(u * W) + (- ((1_ GF) * W)) is right_complementable Element of the carrier of V
the addF of V . ((u * W),(- ((1_ GF) * W))) is right_complementable Element of the carrier of V
[(u * W),(- ((1_ GF) * W))] is set
{(u * W),(- ((1_ GF) * W))} is non empty set
{{(u * W),(- ((1_ GF) * W))},{(u * W)}} is non empty set
the addF of V . [(u * W),(- ((1_ GF) * W))] is set
(u - (1_ GF)) * W is right_complementable Element of the carrier of V
the lmult of V . ((u - (1_ GF)),W) is right_complementable Element of the carrier of V
[(u - (1_ GF)),W] is set
{(u - (1_ GF)),W} is non empty set
{(u - (1_ GF))} is non empty set
{{(u - (1_ GF)),W},{(u - (1_ GF))}} is non empty set
the lmult of V . [(u - (1_ GF)),W] is set
(u - (1_ GF)) " is right_complementable Element of the carrier of GF
((u - (1_ GF)) ") * C is right_complementable Element of the carrier of V
the lmult of V . (((u - (1_ GF)) "),C) is right_complementable Element of the carrier of V
[((u - (1_ GF)) "),C] is set
{((u - (1_ GF)) "),C} is non empty set
{((u - (1_ GF)) ")} is non empty set
{{((u - (1_ GF)) "),C},{((u - (1_ GF)) ")}} is non empty set
the lmult of V . [((u - (1_ GF)) "),C] is set
((u - (1_ GF)) ") * (u - (1_ GF)) is right_complementable Element of the carrier of GF
the multF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
the multF of GF . (((u - (1_ GF)) "),(u - (1_ GF))) is right_complementable Element of the carrier of GF
[((u - (1_ GF)) "),(u - (1_ GF))] is set
{((u - (1_ GF)) "),(u - (1_ GF))} is non empty set
{{((u - (1_ GF)) "),(u - (1_ GF))},{((u - (1_ GF)) ")}} is non empty set
the multF of GF . [((u - (1_ GF)) "),(u - (1_ GF))] is set
(((u - (1_ GF)) ") * (u - (1_ GF))) * W is right_complementable Element of the carrier of V
the lmult of V . ((((u - (1_ GF)) ") * (u - (1_ GF))),W) is right_complementable Element of the carrier of V
[(((u - (1_ GF)) ") * (u - (1_ GF))),W] is set
{(((u - (1_ GF)) ") * (u - (1_ GF))),W} is non empty set
{(((u - (1_ GF)) ") * (u - (1_ GF)))} is non empty set
{{(((u - (1_ GF)) ") * (u - (1_ GF))),W},{(((u - (1_ GF)) ") * (u - (1_ GF)))}} is non empty set
the lmult of V . [(((u - (1_ GF)) ") * (u - (1_ GF))),W] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty set
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of V
u * W is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the lmult of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
the carrier of B is non empty set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
1_ GF is right_complementable Element of the carrier of GF
the carrier of GF is non empty set
1. GF is right_complementable Element of the carrier of GF
the OneF of GF is right_complementable Element of the carrier of GF
- (1_ GF) is right_complementable Element of the carrier of GF
(- (1_ GF)) * u is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((- (1_ GF)),u) is right_complementable Element of the carrier of V
[(- (1_ GF)),u] is set
{(- (1_ GF)),u} is non empty set
{(- (1_ GF))} is non empty set
{{(- (1_ GF)),u},{(- (1_ GF))}} is non empty set
the lmult of V . [(- (1_ GF)),u] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u + W is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,W) is right_complementable Element of the carrier of V
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the addF of V . [u,W] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
W + C is right_complementable Element of the carrier of V
the addF of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of V . [W,C] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
u + (- W) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(- W)) is right_complementable Element of the carrier of V
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of V . [u,(- W)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(- W) + u is right_complementable Element of the carrier of V
the addF of V . ((- W),u) is right_complementable Element of the carrier of V
[(- W),u] is set
{(- W),u} is non empty set
{(- W)} is non empty set
{{(- W),u},{(- W)}} is non empty set
the addF of V . [(- W),u] is set
- (- W) is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
W + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of V . [W,C] is set
- C is right_complementable Element of the carrier of V
C is right_complementable Element of the carrier of V
W - C is right_complementable Element of the carrier of V
- C is right_complementable Element of the carrier of V
W + (- C) is right_complementable Element of the carrier of V
the addF of V . (W,(- C)) is right_complementable Element of the carrier of V
[W,(- C)] is set
{W,(- C)} is non empty set
{{W,(- C)},{W}} is non empty set
the addF of V . [W,(- C)] is set
C is right_complementable Element of the carrier of V
W - C is right_complementable Element of the carrier of V
- C is right_complementable Element of the carrier of V
W + (- C) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,(- C)) is right_complementable Element of the carrier of V
[W,(- C)] is set
{W,(- C)} is non empty set
{W} is non empty set
{{W,(- C)},{W}} is non empty set
the addF of V . [W,(- C)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
u + (- W) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(- W)) is right_complementable Element of the carrier of V
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of V . [u,(- W)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
C is right_complementable Element of the carrier of V
(GF,V,C,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (C + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
C + C is right_complementable Element of the carrier of V
the addF of V . (C,C) is right_complementable Element of the carrier of V
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the addF of V . [C,C] is set
c₈ is right_complementable Element of the carrier of V
C + c₈ is right_complementable Element of the carrier of V
the addF of V . (C,c₈) is right_complementable Element of the carrier of V
[C,c₈] is set
{C,c₈} is non empty set
{{C,c₈},{C}} is non empty set
the addF of V . [C,c₈] is set
c₈ + C is right_complementable Element of the carrier of V
the addF of V . (c₈,C) is right_complementable Element of the carrier of V
[c₈,C] is set
{c₈,C} is non empty set
{c₈} is non empty set
{{c₈,C},{c₈}} is non empty set
the addF of V . [c₈,C] is set
- C is right_complementable Element of the carrier of V
(- C) - C is right_complementable Element of the carrier of V
- C is right_complementable Element of the carrier of V
(- C) + (- C) is right_complementable Element of the carrier of V
the addF of V . ((- C),(- C)) is right_complementable Element of the carrier of V
[(- C),(- C)] is set
{(- C),(- C)} is non empty set
{(- C)} is non empty set
{{(- C),(- C)},{(- C)}} is non empty set
the addF of V . [(- C),(- C)] is set
(c₈ + C) + ((- C) - C) is right_complementable Element of the carrier of V
the addF of V . ((c₈ + C),((- C) - C)) is right_complementable Element of the carrier of V
[(c₈ + C),((- C) - C)] is set
{(c₈ + C),((- C) - C)} is non empty set
{(c₈ + C)} is non empty set
{{(c₈ + C),((- C) - C)},{(c₈ + C)}} is non empty set
the addF of V . [(c₈ + C),((- C) - C)] is set
(c₈ + C) + (- C) is right_complementable Element of the carrier of V
the addF of V . ((c₈ + C),(- C)) is right_complementable Element of the carrier of V
[(c₈ + C),(- C)] is set
{(c₈ + C),(- C)} is non empty set
{{(c₈ + C),(- C)},{(c₈ + C)}} is non empty set
the addF of V . [(c₈ + C),(- C)] is set
((c₈ + C) + (- C)) - C is right_complementable Element of the carrier of V
((c₈ + C) + (- C)) + (- C) is right_complementable Element of the carrier of V
the addF of V . (((c₈ + C) + (- C)),(- C)) is right_complementable Element of the carrier of V
[((c₈ + C) + (- C)),(- C)] is set
{((c₈ + C) + (- C)),(- C)} is non empty set
{((c₈ + C) + (- C))} is non empty set
{{((c₈ + C) + (- C)),(- C)},{((c₈ + C) + (- C))}} is non empty set
the addF of V . [((c₈ + C) + (- C)),(- C)] is set
C + (- C) is right_complementable Element of the carrier of V
the addF of V . (C,(- C)) is right_complementable Element of the carrier of V
[C,(- C)] is set
{C,(- C)} is non empty set
{{C,(- C)},{C}} is non empty set
the addF of V . [C,(- C)] is set
c₈ + (C + (- C)) is right_complementable Element of the carrier of V
the addF of V . (c₈,(C + (- C))) is right_complementable Element of the carrier of V
[c₈,(C + (- C))] is set
{c₈,(C + (- C))} is non empty set
{{c₈,(C + (- C))},{c₈}} is non empty set
the addF of V . [c₈,(C + (- C))] is set
(c₈ + (C + (- C))) - C is right_complementable Element of the carrier of V
(c₈ + (C + (- C))) + (- C) is right_complementable Element of the carrier of V
the addF of V . ((c₈ + (C + (- C))),(- C)) is right_complementable Element of the carrier of V
[(c₈ + (C + (- C))),(- C)] is set
{(c₈ + (C + (- C))),(- C)} is non empty set
{(c₈ + (C + (- C)))} is non empty set
{{(c₈ + (C + (- C))),(- C)},{(c₈ + (C + (- C)))}} is non empty set
the addF of V . [(c₈ + (C + (- C))),(- C)] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
c₈ + (0. V) is right_complementable Element of the carrier of V
the addF of V . (c₈,(0. V)) is right_complementable Element of the carrier of V
[c₈,(0. V)] is set
{c₈,(0. V)} is non empty set
{{c₈,(0. V)},{c₈}} is non empty set
the addF of V . [c₈,(0. V)] is set
(c₈ + (0. V)) - C is right_complementable Element of the carrier of V
(c₈ + (0. V)) + (- C) is right_complementable Element of the carrier of V
the addF of V . ((c₈ + (0. V)),(- C)) is right_complementable Element of the carrier of V
[(c₈ + (0. V)),(- C)] is set
{(c₈ + (0. V)),(- C)} is non empty set
{(c₈ + (0. V))} is non empty set
{{(c₈ + (0. V)),(- C)},{(c₈ + (0. V))}} is non empty set
the addF of V . [(c₈ + (0. V)),(- C)] is set
c₈ - C is right_complementable Element of the carrier of V
c₈ + (- C) is right_complementable Element of the carrier of V
the addF of V . (c₈,(- C)) is right_complementable Element of the carrier of V
[c₈,(- C)] is set
{c₈,(- C)} is non empty set
{{c₈,(- C)},{c₈}} is non empty set
the addF of V . [c₈,(- C)] is set
- (u - W) is right_complementable Element of the carrier of V
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
u + (- (u - W)) is right_complementable Element of the carrier of V
the addF of V . (u,(- (u - W))) is right_complementable Element of the carrier of V
[u,(- (u - W))] is set
{u,(- (u - W))} is non empty set
{{u,(- (u - W))},{u}} is non empty set
the addF of V . [u,(- (u - W))] is set
- u is right_complementable Element of the carrier of V
(- u) + W is right_complementable Element of the carrier of V
the addF of V . ((- u),W) is right_complementable Element of the carrier of V
[(- u),W] is set
{(- u),W} is non empty set
{(- u)} is non empty set
{{(- u),W},{(- u)}} is non empty set
the addF of V . [(- u),W] is set
u + ((- u) + W) is right_complementable Element of the carrier of V
the addF of V . (u,((- u) + W)) is right_complementable Element of the carrier of V
[u,((- u) + W)] is set
{u,((- u) + W)} is non empty set
{{u,((- u) + W)},{u}} is non empty set
the addF of V . [u,((- u) + W)] is set
u + (- u) is right_complementable Element of the carrier of V
the addF of V . (u,(- u)) is right_complementable Element of the carrier of V
[u,(- u)] is set
{u,(- u)} is non empty set
{{u,(- u)},{u}} is non empty set
the addF of V . [u,(- u)] is set
(u + (- u)) + W is right_complementable Element of the carrier of V
the addF of V . ((u + (- u)),W) is right_complementable Element of the carrier of V
[(u + (- u)),W] is set
{(u + (- u)),W} is non empty set
{(u + (- u))} is non empty set
{{(u + (- u)),W},{(u + (- u))}} is non empty set
the addF of V . [(u + (- u)),W] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(0. V) + W is right_complementable Element of the carrier of V
the addF of V . ((0. V),W) is right_complementable Element of the carrier of V
[(0. V),W] is set
{(0. V),W} is non empty set
{(0. V)} is non empty set
{{(0. V),W},{(0. V)}} is non empty set
the addF of V . [(0. V),W] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,W,B) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
W + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (W,C) is right_complementable Element of the carrier of V
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the addF of V . [W,C] is set
W - u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
W + (- u) is right_complementable Element of the carrier of V
the addF of V . (W,(- u)) is right_complementable Element of the carrier of V
[W,(- u)] is set
{W,(- u)} is non empty set
{{W,(- u)},{W}} is non empty set
the addF of V . [W,(- u)] is set
C is right_complementable Element of the carrier of V
u + C is right_complementable Element of the carrier of V
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{u} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(W + C) - u is right_complementable Element of the carrier of V
(W + C) + (- u) is right_complementable Element of the carrier of V
the addF of V . ((W + C),(- u)) is right_complementable Element of the carrier of V
[(W + C),(- u)] is set
{(W + C),(- u)} is non empty set
{(W + C)} is non empty set
{{(W + C),(- u)},{(W + C)}} is non empty set
the addF of V . [(W + C),(- u)] is set
C + (W - u) is right_complementable Element of the carrier of V
the addF of V . (C,(W - u)) is right_complementable Element of the carrier of V
[C,(W - u)] is set
{C,(W - u)} is non empty set
{C} is non empty set
{{C,(W - u)},{C}} is non empty set
the addF of V . [C,(W - u)] is set
- C is right_complementable Element of the carrier of V
W + u is right_complementable Element of the carrier of V
the addF of V . (W,u) is right_complementable Element of the carrier of V
[W,u] is set
{W,u} is non empty set
{{W,u},{W}} is non empty set
the addF of V . [W,u] is set
(W + u) - u is right_complementable Element of the carrier of V
(W + u) + (- u) is right_complementable Element of the carrier of V
the addF of V . ((W + u),(- u)) is right_complementable Element of the carrier of V
[(W + u),(- u)] is set
{(W + u),(- u)} is non empty set
{(W + u)} is non empty set
{{(W + u),(- u)},{(W + u)}} is non empty set
the addF of V . [(W + u),(- u)] is set
u - u is right_complementable Element of the carrier of V
u + (- u) is right_complementable Element of the carrier of V
the addF of V . (u,(- u)) is right_complementable Element of the carrier of V
[u,(- u)] is set
{u,(- u)} is non empty set
{{u,(- u)},{u}} is non empty set
the addF of V . [u,(- u)] is set
W + (u - u) is right_complementable Element of the carrier of V
the addF of V . (W,(u - u)) is right_complementable Element of the carrier of V
[W,(u - u)] is set
{W,(u - u)} is non empty set
{{W,(u - u)},{W}} is non empty set
the addF of V . [W,(u - u)] is set
W + (0. V) is right_complementable Element of the carrier of V
the addF of V . (W,(0. V)) is right_complementable Element of the carrier of V
[W,(0. V)] is set
{W,(0. V)} is non empty set
{{W,(0. V)},{W}} is non empty set
the addF of V . [W,(0. V)] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,W,B) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
u + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{u} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
u - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
u + (- W) is right_complementable Element of the carrier of V
the addF of V . (u,(- W)) is right_complementable Element of the carrier of V
[u,(- W)] is set
{u,(- W)} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of V . [u,(- W)] is set
C is right_complementable Element of the carrier of V
u - C is right_complementable Element of the carrier of V
- C is right_complementable Element of the carrier of V
u + (- C) is right_complementable Element of the carrier of V
the addF of V . (u,(- C)) is right_complementable Element of the carrier of V
[u,(- C)] is set
{u,(- C)} is non empty set
{{u,(- C)},{u}} is non empty set
the addF of V . [u,(- C)] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(u + C) - W is right_complementable Element of the carrier of V
(u + C) + (- W) is right_complementable Element of the carrier of V
the addF of V . ((u + C),(- W)) is right_complementable Element of the carrier of V
[(u + C),(- W)] is set
{(u + C),(- W)} is non empty set
{(u + C)} is non empty set
{{(u + C),(- W)},{(u + C)}} is non empty set
the addF of V . [(u + C),(- W)] is set
C + (u - W) is right_complementable Element of the carrier of V
the addF of V . (C,(u - W)) is right_complementable Element of the carrier of V
[C,(u - W)] is set
{C,(u - W)} is non empty set
{C} is non empty set
{{C,(u - W)},{C}} is non empty set
the addF of V . [C,(u - W)] is set
- C is right_complementable Element of the carrier of V
u - u is right_complementable Element of the carrier of V
- u is right_complementable Element of the carrier of V
u + (- u) is right_complementable Element of the carrier of V
the addF of V . (u,(- u)) is right_complementable Element of the carrier of V
[u,(- u)] is set
{u,(- u)} is non empty set
{{u,(- u)},{u}} is non empty set
the addF of V . [u,(- u)] is set
(u - u) + W is right_complementable Element of the carrier of V
the addF of V . ((u - u),W) is right_complementable Element of the carrier of V
[(u - u),W] is set
{(u - u),W} is non empty set
{(u - u)} is non empty set
{{(u - u),W},{(u - u)}} is non empty set
the addF of V . [(u - u),W] is set
(0. V) + W is right_complementable Element of the carrier of V
the addF of V . ((0. V),W) is right_complementable Element of the carrier of V
[(0. V),W] is set
{(0. V),W} is non empty set
{(0. V)} is non empty set
{{(0. V),W},{(0. V)}} is non empty set
the addF of V . [(0. V),W] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
B is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,B) is Element of bool the carrier of V
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
the carrier of W is non empty set
the carrier of B is non empty set
C is set
C is right_complementable Element of the carrier of V
u + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{u} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
x is right_complementable Element of the carrier of V
u + x is right_complementable Element of the carrier of V
the addF of V . (u,x) is right_complementable Element of the carrier of V
[u,x] is set
{u,x} is non empty set
{{u,x},{u}} is non empty set
the addF of V . [u,x] is set
C is set
C is right_complementable Element of the carrier of V
u + C is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,C) is right_complementable Element of the carrier of V
[u,C] is set
{u,C} is non empty set
{u} is non empty set
{{u,C},{u}} is non empty set
the addF of V . [u,C] is set
x is right_complementable Element of the carrier of V
u + x is right_complementable Element of the carrier of V
the addF of V . (u,x) is right_complementable Element of the carrier of V
[u,x] is set
{u,x} is non empty set
{{u,x},{u}} is non empty set
the addF of V . [u,x] is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,W,C) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
the carrier of C is non empty set
the carrier of B is non empty set
the carrier of B \ the carrier of C is Element of bool the carrier of B
bool the carrier of B is non empty set
the Element of the carrier of B \ the carrier of C is Element of the carrier of B \ the carrier of C
x is right_complementable Element of the carrier of V
u + x is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,x) is right_complementable Element of the carrier of V
[u,x] is set
{u,x} is non empty set
{u} is non empty set
{{u,x},{u}} is non empty set
the addF of V . [u,x] is set
u1 is right_complementable Element of the carrier of V
W + u1 is right_complementable Element of the carrier of V
the addF of V . (W,u1) is right_complementable Element of the carrier of V
[W,u1] is set
{W,u1} is non empty set
{W} is non empty set
{{W,u1},{W}} is non empty set
the addF of V . [W,u1] is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(0. V) + x is right_complementable Element of the carrier of V
the addF of V . ((0. V),x) is right_complementable Element of the carrier of V
[(0. V),x] is set
{(0. V),x} is non empty set
{(0. V)} is non empty set
{{(0. V),x},{(0. V)}} is non empty set
the addF of V . [(0. V),x] is set
- u is right_complementable Element of the carrier of V
u + (- u) is right_complementable Element of the carrier of V
the addF of V . (u,(- u)) is right_complementable Element of the carrier of V
[u,(- u)] is set
{u,(- u)} is non empty set
{{u,(- u)},{u}} is non empty set
the addF of V . [u,(- u)] is set
(u + (- u)) + x is right_complementable Element of the carrier of V
the addF of V . ((u + (- u)),x) is right_complementable Element of the carrier of V
[(u + (- u)),x] is set
{(u + (- u)),x} is non empty set
{(u + (- u))} is non empty set
{{(u + (- u)),x},{(u + (- u))}} is non empty set
the addF of V . [(u + (- u)),x] is set
(- u) + (W + u1) is right_complementable Element of the carrier of V
the addF of V . ((- u),(W + u1)) is right_complementable Element of the carrier of V
[(- u),(W + u1)] is set
{(- u),(W + u1)} is non empty set
{(- u)} is non empty set
{{(- u),(W + u1)},{(- u)}} is non empty set
the addF of V . [(- u),(W + u1)] is set
u + ((- u) + (W + u1)) is right_complementable Element of the carrier of V
the addF of V . (u,((- u) + (W + u1))) is right_complementable Element of the carrier of V
[u,((- u) + (W + u1))] is set
{u,((- u) + (W + u1))} is non empty set
{{u,((- u) + (W + u1))},{u}} is non empty set
the addF of V . [u,((- u) + (W + u1))] is set
(GF,V,(u + ((- u) + (W + u1))),B) is Element of bool the carrier of V
{ ((u + ((- u) + (W + u1))) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(u + (- u)) + (W + u1) is right_complementable Element of the carrier of V
the addF of V . ((u + (- u)),(W + u1)) is right_complementable Element of the carrier of V
[(u + (- u)),(W + u1)] is set
{(u + (- u)),(W + u1)} is non empty set
{{(u + (- u)),(W + u1)},{(u + (- u))}} is non empty set
the addF of V . [(u + (- u)),(W + u1)] is set
(0. V) + (W + u1) is right_complementable Element of the carrier of V
the addF of V . ((0. V),(W + u1)) is right_complementable Element of the carrier of V
[(0. V),(W + u1)] is set
{(0. V),(W + u1)} is non empty set
{{(0. V),(W + u1)},{(0. V)}} is non empty set
the addF of V . [(0. V),(W + u1)] is set
(GF,V,(W + u1),C) is Element of bool the carrier of V
{ ((W + u1) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
(GF,V,(W + u1),B) is Element of bool the carrier of V
{ ((W + u1) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
the carrier of C \ the carrier of B is Element of bool the carrier of C
bool the carrier of C is non empty set
the Element of the carrier of C \ the carrier of B is Element of the carrier of C \ the carrier of B
x is right_complementable Element of the carrier of V
W + x is right_complementable Element of the carrier of V
the addF of V . (W,x) is right_complementable Element of the carrier of V
[W,x] is set
{W,x} is non empty set
{{W,x},{W}} is non empty set
the addF of V . [W,x] is set
u1 is right_complementable Element of the carrier of V
u + u1 is right_complementable Element of the carrier of V
the addF of V . (u,u1) is right_complementable Element of the carrier of V
[u,u1] is set
{u,u1} is non empty set
{{u,u1},{u}} is non empty set
the addF of V . [u,u1] is set
(0. V) + x is right_complementable Element of the carrier of V
the addF of V . ((0. V),x) is right_complementable Element of the carrier of V
[(0. V),x] is set
{(0. V),x} is non empty set
{{(0. V),x},{(0. V)}} is non empty set
the addF of V . [(0. V),x] is set
- W is right_complementable Element of the carrier of V
W + (- W) is right_complementable Element of the carrier of V
the addF of V . (W,(- W)) is right_complementable Element of the carrier of V
[W,(- W)] is set
{W,(- W)} is non empty set
{{W,(- W)},{W}} is non empty set
the addF of V . [W,(- W)] is set
(W + (- W)) + x is right_complementable Element of the carrier of V
the addF of V . ((W + (- W)),x) is right_complementable Element of the carrier of V
[(W + (- W)),x] is set
{(W + (- W)),x} is non empty set
{(W + (- W))} is non empty set
{{(W + (- W)),x},{(W + (- W))}} is non empty set
the addF of V . [(W + (- W)),x] is set
(- W) + (u + u1) is right_complementable Element of the carrier of V
the addF of V . ((- W),(u + u1)) is right_complementable Element of the carrier of V
[(- W),(u + u1)] is set
{(- W),(u + u1)} is non empty set
{(- W)} is non empty set
{{(- W),(u + u1)},{(- W)}} is non empty set
the addF of V . [(- W),(u + u1)] is set
W + ((- W) + (u + u1)) is right_complementable Element of the carrier of V
the addF of V . (W,((- W) + (u + u1))) is right_complementable Element of the carrier of V
[W,((- W) + (u + u1))] is set
{W,((- W) + (u + u1))} is non empty set
{{W,((- W) + (u + u1))},{W}} is non empty set
the addF of V . [W,((- W) + (u + u1))] is set
(GF,V,(W + ((- W) + (u + u1))),C) is Element of bool the carrier of V
{ ((W + ((- W) + (u + u1))) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
(W + (- W)) + (u + u1) is right_complementable Element of the carrier of V
the addF of V . ((W + (- W)),(u + u1)) is right_complementable Element of the carrier of V
[(W + (- W)),(u + u1)] is set
{(W + (- W)),(u + u1)} is non empty set
{{(W + (- W)),(u + u1)},{(W + (- W))}} is non empty set
the addF of V . [(W + (- W)),(u + u1)] is set
(0. V) + (u + u1) is right_complementable Element of the carrier of V
the addF of V . ((0. V),(u + u1)) is right_complementable Element of the carrier of V
[(0. V),(u + u1)] is set
{(0. V),(u + u1)} is non empty set
{{(0. V),(u + u1)},{(0. V)}} is non empty set
the addF of V . [(0. V),(u + u1)] is set
(GF,V,(u + u1),B) is Element of bool the carrier of V
{ ((u + u1) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,(u + u1),C) is Element of bool the carrier of V
{ ((u + u1) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in C } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
B is (GF,V,W)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is (GF,V,u)
the carrier of V is non empty set
B is right_complementable Element of the carrier of V
(GF,V,B,u) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (B + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
0. V is V49(V) right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
W is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
B is (GF,V,u)
C is (GF,V,W)
the carrier of V is non empty set
C is right_complementable Element of the carrier of V
(GF,V,C,u) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (C + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
c₈ is right_complementable Element of the carrier of V
(GF,V,c₈,W) is Element of bool the carrier of V
{ (c₈ + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
u is right_complementable Element of the carrier of V
{u} is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
(GF,V,u,(GF,V)) is Element of bool the carrier of V
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in (GF,V) } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
u is Element of bool the carrier of V
W is right_complementable Element of the carrier of V
(GF,V,W,(GF,V)) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in (GF,V) } is set
{W} is non empty Element of bool the carrier of V
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
(GF,V,(0. V),u) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((0. V) + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty strict VectSpStr over GF
the right_complementable Element of the carrier of V is right_complementable Element of the carrier of V
bool the carrier of V is non empty set
W is Element of bool the carrier of V
(GF,V, the right_complementable Element of the carrier of V,(GF,V)) is Element of bool the carrier of V
{ ( the right_complementable Element of the carrier of V + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in (GF,V) } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
bool the carrier of V is non empty set
(GF,V) is non empty right_complementable strict vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
the carrier of GF is non empty set
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
VectSpStr(# the carrier of V, the addF of V, the ZeroF of V, the lmult of V #) is non empty strict VectSpStr over GF
u is Element of bool the carrier of V
W is right_complementable Element of the carrier of V
(GF,V,W,(GF,V)) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in (GF,V) } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
0. V is V49(V) right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
u is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
the carrier of u is non empty set
W is (GF,V,u)
B is right_complementable Element of the carrier of V
(GF,V,B,u) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (B + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in u } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
(GF,V,u,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
B is (GF,V,W)
C is right_complementable Element of the carrier of V
(GF,V,C,W) is Element of bool the carrier of V
{ (C + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
C is (GF,V,B)
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,W,B) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
C is (GF,V,B)
(GF,V,u,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
(GF,V,W,B) is Element of bool the carrier of V
{ (W + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is right_complementable Element of the carrier of V
u - W is right_complementable Element of the carrier of V
- W is right_complementable Element of the carrier of V
u + (- W) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (u,(- W)) is right_complementable Element of the carrier of V
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of V . [u,(- W)] is set
B is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
C is (GF,V,B)
C is right_complementable Element of the carrier of V
(GF,V,C,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (C + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is right_complementable Element of the carrier of V
(GF,V,C,B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (C + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in B } is set
C is (GF,V,B)
GF is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of V
W is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed (GF,V)
B is (GF,V,W)
C is (GF,V,W)
C is right_complementable Element of the carrier of V
(GF,V,C,W) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (C + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
c₈ is right_complementable Element of the carrier of V
(GF,V,c₈,W) is Element of bool the carrier of V
{ (c₈ + b₁) where b₁ is right_complementable Element of the carrier of V : b₁ in W } is set
GF is non empty right_complementable unital associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of GF is non empty set
V is non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed VectSpStr over GF
the carrier of V is non empty set
u is right_complementable Element of the carrier of GF
W is right_complementable Element of the carrier of GF
u - W is right_complementable Element of the carrier of GF
- W is right_complementable Element of the carrier of GF
u + (- W) is right_complementable Element of the carrier of GF
the addF of GF is Relation-like Function-like V18([: the carrier of GF, the carrier of GF:], the carrier of GF) Element of bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:]
[: the carrier of GF, the carrier of GF:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of GF:], the carrier of GF:] is non empty set
the addF of GF . (u,(- W)) is right_complementable Element of the carrier of GF
[u,(- W)] is set
{u,(- W)} is non empty set
{u} is non empty set
{{u,(- W)},{u}} is non empty set
the addF of GF . [u,(- W)] is set
B is right_complementable Element of the carrier of V
(u - W) * B is right_complementable Element of the carrier of V
the lmult of V is Relation-like Function-like V18([: the carrier of GF, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of GF, the carrier of V:], the carrier of V:]
[: the carrier of GF, the carrier of V:] is Relation-like non empty set
[:[: the carrier of GF, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of GF, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((u - W),B) is right_complementable Element of the carrier of V
[(u - W),B] is set
{(u - W),B} is non empty set
{(u - W)} is non empty set
{{(u - W),B},{(u - W)}} is non empty set
the lmult of V . [(u - W),B] is set
u * B is right_complementable Element of the carrier of V
the lmult of V . (u,B) is right_complementable Element of the carrier of V
[u,B] is set
{u,B} is non empty set
{{u,B},{u}} is non empty set
the lmult of V . [u,B] is set
W * B is right_complementable Element of the carrier of V
the lmult of V . (W,B) is right_complementable Element of the carrier of V
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the lmult of V . [W,B] is set
(u * B) - (W * B) is right_complementable Element of the carrier of V
- (W * B) is right_complementable Element of the carrier of V
(u * B) + (- (W * B)) is right_complementable Element of the carrier of V
the addF of V is Relation-like Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((u * B),(- (W * B))) is right_complementable Element of the carrier of V
[(u * B),(- (W * B))] is set
{(u * B),(- (W * B))} is non empty set
{(u * B)} is non empty set
{{(u * B),(- (W * B))},{(u * B)}} is non empty set
the addF of V . [(u * B),(- (W * B))] is set