REAL is non empty V36() set
NAT is non empty epsilon-transitive epsilon-connected ordinal Element of bool REAL
bool REAL is non empty set
NAT is non empty epsilon-transitive epsilon-connected ordinal set
bool NAT is non empty set
bool NAT is non empty set
{} is Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() real V33() set
the Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() real V33() set is Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() real V33() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() real V33() Element of NAT
0 is Function-like functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() real V33() Element of NAT
- 1 is V31() real V33() Element of REAL
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is Element of bool the carrier of V
the Element of u is Element of u
B is left_complementable right_complementable complementable Element of the carrier of V
0 * B is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (0,B) is set
[0,B] is set
{0,B} is non empty set
{0} is non empty set
{{0,B},{0}} is non empty set
the Mult of V . [0,B] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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 left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
(- 1) * W is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . ((- 1),W) is set
[(- 1),W] is set
{(- 1),W} is non empty set
{(- 1)} is non empty set
{{(- 1),W},{(- 1)}} is non empty set
the Mult of V . [(- 1),W] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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 left_complementable right_complementable complementable Element of the carrier of V
B is left_complementable right_complementable complementable Element of the carrier of V
W - B is left_complementable right_complementable complementable Element of the carrier of V
- B is left_complementable right_complementable complementable Element of the carrier of V
W + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u + W is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 is V31() real V33() Element of REAL
W is left_complementable right_complementable complementable Element of the carrier of V
u * W is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (u,W) is set
[u,W] is set
{u,W} is non empty set
{u} is non empty set
{{u,W},{u}} is non empty set
the Mult of V . [u,W] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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 left_complementable right_complementable complementable Element of the carrier of V
B is left_complementable right_complementable complementable Element of the carrier of V
W + B is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
W is V31() real V33() Element of REAL
B is left_complementable right_complementable complementable Element of the carrier of V
W * B is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,B) is set
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the Mult of V . [W,B] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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
{ (b1 + b2) where b1, b2 is left_complementable right_complementable complementable Element of the carrier of V : ( b1 in u & b2 in W ) } is set
B is Element of bool the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
C + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
c7 is left_complementable right_complementable complementable Element of the carrier of V
x is left_complementable right_complementable complementable Element of the carrier of V
c7 + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,x) is left_complementable right_complementable complementable Element of the carrier of V
[c7,x] is set
{c7,x} is non empty set
{c7} is non empty set
{{c7,x},{c7}} is non empty set
the addF of V . [c7,x] is set
x is left_complementable right_complementable complementable Element of the carrier of V
z is left_complementable right_complementable complementable Element of the carrier of V
x + z is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (x,z) is left_complementable right_complementable 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
(c7 + x) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + x),x) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + x),x] is set
{(c7 + x),x} is non empty set
{(c7 + x)} is non empty set
{{(c7 + x),x},{(c7 + x)}} is non empty set
the addF of V . [(c7 + x),x] is set
((c7 + x) + x) + z is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (((c7 + x) + x),z) is left_complementable right_complementable complementable Element of the carrier of V
[((c7 + x) + x),z] is set
{((c7 + x) + x),z} is non empty set
{((c7 + x) + x)} is non empty set
{{((c7 + x) + x),z},{((c7 + x) + x)}} is non empty set
the addF of V . [((c7 + x) + x),z] is set
c7 + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,x) is left_complementable right_complementable complementable Element of the carrier of V
[c7,x] is set
{c7,x} is non empty set
{{c7,x},{c7}} is non empty set
the addF of V . [c7,x] is set
(c7 + x) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + x),x) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + x),x] is set
{(c7 + x),x} is non empty set
{(c7 + x)} is non empty set
{{(c7 + x),x},{(c7 + x)}} is non empty set
the addF of V . [(c7 + x),x] is set
((c7 + x) + x) + z is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (((c7 + x) + x),z) is left_complementable right_complementable complementable Element of the carrier of V
[((c7 + x) + x),z] is set
{((c7 + x) + x),z} is non empty set
{((c7 + x) + x)} is non empty set
{{((c7 + x) + x),z},{((c7 + x) + x)}} is non empty set
the addF of V . [((c7 + x) + x),z] is set
x + z is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (x,z) is left_complementable right_complementable 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
(c7 + x) + (x + z) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + x),(x + z)) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + x),(x + z)] is set
{(c7 + x),(x + z)} is non empty set
{{(c7 + x),(x + z)},{(c7 + x)}} is non empty set
the addF of V . [(c7 + x),(x + z)] is set
C is V31() real V33() Element of REAL
C is left_complementable right_complementable complementable Element of the carrier of V
C * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (C,C) is set
[C,C] is set
{C,C} is non empty set
{C} is non empty set
{{C,C},{C}} is non empty set
the Mult of V . [C,C] is set
c7 is left_complementable right_complementable complementable Element of the carrier of V
x is left_complementable right_complementable complementable Element of the carrier of V
c7 + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (c7,x) is left_complementable right_complementable complementable Element of the carrier of V
[c7,x] is set
{c7,x} is non empty set
{c7} is non empty set
{{c7,x},{c7}} is non empty set
the addF of V . [c7,x] is set
C * c7 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (C,c7) is set
[C,c7] is set
{C,c7} is non empty set
{{C,c7},{C}} is non empty set
the Mult of V . [C,c7] is set
C * x is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (C,x) is set
[C,x] is set
{C,x} is non empty set
{{C,x},{C}} is non empty set
the Mult of V . [C,x] is set
(C * c7) + (C * x) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((C * c7),(C * x)) is left_complementable right_complementable complementable Element of the carrier of V
[(C * c7),(C * x)] is set
{(C * c7),(C * x)} is non empty set
{(C * c7)} is non empty set
{{(C * c7),(C * x)},{(C * c7)}} is non empty set
the addF of V . [(C * c7),(C * x)] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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 left_complementable right_complementable complementable Element of the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
B + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
B is V31() real V33() Element of REAL
C is left_complementable right_complementable complementable Element of the carrier of V
B * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (B,C) is set
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the Mult of V . [B,C] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, 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 Mult of V | [:REAL, the carrier of V:] is Relation-like Function-like set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is set
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
the carrier of B is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is set
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
the carrier of V is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is left_complementable right_complementable complementable Element of the carrier of u
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. W is V55(W) left_complementable right_complementable complementable Element of the carrier of W
the carrier of W is non empty set
the ZeroF of W is left_complementable right_complementable complementable Element of the carrier of W
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u + W is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of B is non empty set
C is left_complementable right_complementable complementable Element of the carrier of B
C is left_complementable right_complementable complementable Element of the carrier of B
C + C is left_complementable right_complementable complementable Element of the carrier of B
the addF of B is Relation-like [: the carrier of B, the carrier of B:] -defined the carrier of B -valued 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 non empty set
[:[: the carrier of B, the carrier of B:], the carrier of B:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is V31() real V33() Element of REAL
W * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,u) is set
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the Mult of V . [W,u] is set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of B is non empty set
C is left_complementable right_complementable complementable Element of the carrier of B
W * C is left_complementable right_complementable complementable Element of the carrier of B
the Mult of B is Relation-like [:REAL, the carrier of B:] -defined the carrier of B -valued Function-like V18([:REAL, the carrier of B:], the carrier of B) Element of bool [:[:REAL, the carrier of B:], the carrier of B:]
[:REAL, the carrier of B:] is non empty set
[:[:REAL, the carrier of B:], the carrier of B:] is non empty set
bool [:[:REAL, the carrier of B:], the carrier of B:] is non empty set
the Mult of B . (W,C) is set
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the Mult of B . [W,C] is set
the Mult of V | [:REAL, the carrier of B:] is Relation-like Function-like set
[W,C] is Element of [:REAL, the carrier of B:]
( the Mult of V | [:REAL, the carrier of B:]) . [W,C] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
B is left_complementable right_complementable complementable Element of the carrier of W
- B is left_complementable right_complementable complementable Element of the carrier of W
(- 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . ((- 1),u) is set
[(- 1),u] is set
{(- 1),u} is non empty set
{(- 1)} is non empty set
{{(- 1),u},{(- 1)}} is non empty set
the Mult of V . [(- 1),u] is set
(- 1) * B is left_complementable right_complementable complementable Element of the carrier of W
the Mult of W is Relation-like [:REAL, the carrier of W:] -defined the carrier of W -valued Function-like V18([:REAL, the carrier of W:], the carrier of W) Element of bool [:[:REAL, the carrier of W:], the carrier of W:]
[:REAL, the carrier of W:] is non empty set
[:[:REAL, the carrier of W:], the carrier of W:] is non empty set
bool [:[:REAL, the carrier of W:], the carrier of W:] is non empty set
the Mult of W . ((- 1),B) is set
[(- 1),B] is set
{(- 1),B} is non empty set
{{(- 1),B},{(- 1)}} is non empty set
the Mult of W . [(- 1),B] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u - W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
u + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of B is non empty set
C is left_complementable right_complementable complementable Element of the carrier of B
C is left_complementable right_complementable complementable Element of the carrier of B
C - C is left_complementable right_complementable complementable Element of the carrier of B
- C is left_complementable right_complementable complementable Element of the carrier of B
C + (- C) is left_complementable right_complementable complementable Element of the carrier of B
the addF of B is Relation-like [: the carrier of B, the carrier of B:] -defined the carrier of B -valued 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 non empty set
[:[: the carrier of B, the carrier of B:], the carrier of B:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
C is left_complementable right_complementable complementable Element of the carrier of V
c7 is left_complementable right_complementable complementable Element of the carrier of V
C + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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,c7) is left_complementable right_complementable complementable Element of the carrier of V
[C,c7] is set
{C,c7} is non empty set
{C} is non empty set
{{C,c7},{C}} is non empty set
the addF of V . [C,c7] is set
C is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of C is non empty set
x is left_complementable right_complementable complementable Element of the carrier of C
x is left_complementable right_complementable complementable Element of the carrier of C
x + x is left_complementable right_complementable complementable Element of the carrier of C
the addF of C is Relation-like [: the carrier of C, the carrier of C:] -defined the carrier of C -valued 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 non empty set
[:[: the carrier of C, the carrier of C:], the carrier of C:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of W
C is V31() real V33() Element of REAL
c7 is left_complementable right_complementable complementable Element of the carrier of V
C * c7 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (C,c7) is set
[C,c7] is set
{C,c7} is non empty set
{C} is non empty set
{{C,c7},{C}} is non empty set
the Mult of V . [C,c7] is set
C is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of C is non empty set
x is left_complementable right_complementable complementable Element of the carrier of C
C * x is left_complementable right_complementable complementable Element of the carrier of C
the Mult of C is Relation-like [:REAL, the carrier of C:] -defined the carrier of C -valued Function-like V18([:REAL, the carrier of C:], the carrier of C) Element of bool [:[:REAL, the carrier of C:], the carrier of C:]
[:REAL, the carrier of C:] is non empty set
[:[:REAL, the carrier of C:], the carrier of C:] is non empty set
bool [:[:REAL, the carrier of C:], the carrier of C:] is non empty set
the Mult of C . (C,x) is set
[C,x] is set
{C,x} is non empty set
{{C,x},{C}} is non empty set
the Mult of C . [C,x] is set
x is left_complementable right_complementable complementable Element of the carrier of W
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the carrier of u is non empty set
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u + W is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is V31() real V33() Element of REAL
W * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,u) is set
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the Mult of V . [W,u] is set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(- 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . ((- 1),u) is set
[(- 1),u] is set
{(- 1),u} is non empty set
{(- 1)} is non empty set
{{(- 1),u},{(- 1)}} is non empty set
the Mult of V . [(- 1),u] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u - W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
u + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
u is Element of bool the carrier of V
the addF of V || u is Relation-like Function-like set
[:u,u:] is set
the addF of V | [:u,u:] is Relation-like Function-like set
[:REAL,u:] is set
the Mult of V | [:REAL,u:] is Relation-like Function-like set
W is non empty set
[:W,W:] is non empty set
[:[:W,W:],W:] is non empty set
bool [:[:W,W:],W:] is non empty set
[:REAL,W:] is non empty set
[:[:REAL,W:],W:] is non empty set
bool [:[:REAL,W:],W:] is non empty set
B is Element of W
C is Relation-like [:W,W:] -defined W -valued Function-like V18([:W,W:],W) Element of bool [:[:W,W:],W:]
C is Relation-like [:REAL,W:] -defined W -valued Function-like V18([:REAL,W:],W) Element of bool [:[:REAL,W:],W:]
RLSStruct(# W,B,C,C #) is non empty strict RLSStruct
the carrier of RLSStruct(# W,B,C,C #) is non empty set
x is V31() real V33() Element of REAL
x is Element of the carrier of RLSStruct(# W,B,C,C #)
x * x is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) is Relation-like [:REAL, the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[:REAL, the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the Mult of RLSStruct(# W,B,C,C #) . (x,x) is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [x,x] is set
the Mult of V . (x,x) is set
the Mult of V . [x,x] is set
[x,x] is Element of [:REAL, the carrier of RLSStruct(# W,B,C,C #):]
the Mult of V . [x,x] is set
x is Element of the carrier of RLSStruct(# W,B,C,C #)
x is Element of the carrier of RLSStruct(# W,B,C,C #)
x + x is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . (x,x) is Element of the carrier of RLSStruct(# W,B,C,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 RLSStruct(# W,B,C,C #) . [x,x] is set
the addF of V . (x,x) is set
the addF of V . [x,x] is set
[x,x] is Element of [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):]
the addF of V . [x,x] is set
z is Element of the carrier of RLSStruct(# W,B,C,C #)
u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
z + u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . (z,u1) is Element of the carrier of RLSStruct(# W,B,C,C #)
[z,u1] is set
{z,u1} is non empty set
{z} is non empty set
{{z,u1},{z}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [z,u1] is set
u1 + z is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . (u1,z) is Element of the carrier of RLSStruct(# W,B,C,C #)
[u1,z] is set
{u1,z} is non empty set
{u1} is non empty set
{{u1,z},{u1}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [u1,z] is set
x2 is left_complementable right_complementable complementable Element of the carrier of V
v1 is left_complementable right_complementable complementable Element of the carrier of V
x2 + v1 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (x2,v1) is left_complementable right_complementable complementable Element of the carrier of V
[x2,v1] is set
{x2,v1} is non empty set
{x2} is non empty set
{{x2,v1},{x2}} is non empty set
the addF of V . [x2,v1] is set
v1 + x2 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (v1,x2) is left_complementable right_complementable complementable Element of the carrier of V
[v1,x2] is set
{v1,x2} is non empty set
{v1} is non empty set
{{v1,x2},{v1}} is non empty set
the addF of V . [v1,x2] is set
z is Element of the carrier of RLSStruct(# W,B,C,C #)
u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
z + u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . (z,u1) is Element of the carrier of RLSStruct(# W,B,C,C #)
[z,u1] is set
{z,u1} is non empty set
{z} is non empty set
{{z,u1},{z}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [z,u1] is set
x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
(z + u1) + x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . ((z + u1),x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
[(z + u1),x2] is set
{(z + u1),x2} is non empty set
{(z + u1)} is non empty set
{{(z + u1),x2},{(z + u1)}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [(z + u1),x2] is set
u1 + x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . (u1,x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
[u1,x2] is set
{u1,x2} is non empty set
{u1} is non empty set
{{u1,x2},{u1}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [u1,x2] is set
z + (u1 + x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . (z,(u1 + x2)) is Element of the carrier of RLSStruct(# W,B,C,C #)
[z,(u1 + x2)] is set
{z,(u1 + x2)} is non empty set
{{z,(u1 + x2)},{z}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [z,(u1 + x2)] is set
b is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((z + u1),b) is set
[(z + u1),b] is set
{(z + u1),b} is non empty set
{{(z + u1),b},{(z + u1)}} is non empty set
the addF of V . [(z + u1),b] is set
v1 is left_complementable right_complementable complementable Element of the carrier of V
v2 is left_complementable right_complementable complementable Element of the carrier of V
v1 + v2 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (v1,v2) is left_complementable right_complementable complementable Element of the carrier of V
[v1,v2] is set
{v1,v2} is non empty set
{v1} is non empty set
{{v1,v2},{v1}} is non empty set
the addF of V . [v1,v2] is set
(v1 + v2) + b is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((v1 + v2),b) is left_complementable right_complementable complementable Element of the carrier of V
[(v1 + v2),b] is set
{(v1 + v2),b} is non empty set
{(v1 + v2)} is non empty set
{{(v1 + v2),b},{(v1 + v2)}} is non empty set
the addF of V . [(v1 + v2),b] is set
v2 + b is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (v2,b) is left_complementable right_complementable complementable Element of the carrier of V
[v2,b] is set
{v2,b} is non empty set
{v2} is non empty set
{{v2,b},{v2}} is non empty set
the addF of V . [v2,b] is set
v1 + (v2 + b) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (v1,(v2 + b)) is left_complementable right_complementable complementable Element of the carrier of V
[v1,(v2 + b)] is set
{v1,(v2 + b)} is non empty set
{{v1,(v2 + b)},{v1}} is non empty set
the addF of V . [v1,(v2 + b)] is set
the addF of V . (v1,(u1 + x2)) is set
[v1,(u1 + x2)] is set
{v1,(u1 + x2)} is non empty set
{{v1,(u1 + x2)},{v1}} is non empty set
the addF of V . [v1,(u1 + x2)] is set
z is Element of the carrier of RLSStruct(# W,B,C,C #)
0. RLSStruct(# W,B,C,C #) is V55( RLSStruct(# W,B,C,C #)) Element of the carrier of RLSStruct(# W,B,C,C #)
the ZeroF of RLSStruct(# W,B,C,C #) is Element of the carrier of RLSStruct(# W,B,C,C #)
z + (0. RLSStruct(# W,B,C,C #)) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . (z,(0. RLSStruct(# W,B,C,C #))) is Element of the carrier of RLSStruct(# W,B,C,C #)
[z,(0. RLSStruct(# W,B,C,C #))] is set
{z,(0. RLSStruct(# W,B,C,C #))} is non empty set
{z} is non empty set
{{z,(0. RLSStruct(# W,B,C,C #))},{z}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [z,(0. RLSStruct(# W,B,C,C #))] is set
u1 is left_complementable right_complementable complementable Element of the carrier of V
u1 + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u1,(0. V)) is left_complementable right_complementable complementable Element of the carrier of V
[u1,(0. V)] is set
{u1,(0. V)} is non empty set
{u1} is non empty set
{{u1,(0. V)},{u1}} is non empty set
the addF of V . [u1,(0. V)] is set
z is Element of the carrier of RLSStruct(# W,B,C,C #)
u1 is left_complementable right_complementable complementable Element of the carrier of V
x2 is left_complementable right_complementable complementable Element of the carrier of V
u1 + x2 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u1,x2) is left_complementable right_complementable complementable Element of the carrier of V
[u1,x2] is set
{u1,x2} is non empty set
{u1} is non empty set
{{u1,x2},{u1}} is non empty set
the addF of V . [u1,x2] is set
- u1 is left_complementable right_complementable complementable Element of the carrier of V
(- 1) * u1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((- 1),u1) is set
[(- 1),u1] is set
{(- 1),u1} is non empty set
{(- 1)} is non empty set
{{(- 1),u1},{(- 1)}} is non empty set
the Mult of V . [(- 1),u1] is set
(- 1) * z is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) is Relation-like [:REAL, the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[:REAL, the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the Mult of RLSStruct(# W,B,C,C #) . ((- 1),z) is set
[(- 1),z] is set
{(- 1),z} is non empty set
{{(- 1),z},{(- 1)}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [(- 1),z] is set
v1 is Element of the carrier of RLSStruct(# W,B,C,C #)
z + v1 is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . (z,v1) is Element of the carrier of RLSStruct(# W,B,C,C #)
[z,v1] is set
{z,v1} is non empty set
{z} is non empty set
{{z,v1},{z}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [z,v1] is set
0. RLSStruct(# W,B,C,C #) is V55( RLSStruct(# W,B,C,C #)) Element of the carrier of RLSStruct(# W,B,C,C #)
the ZeroF of RLSStruct(# W,B,C,C #) is Element of the carrier of RLSStruct(# W,B,C,C #)
z is V31() real V33() set
u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
u1 + x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . (u1,x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
[u1,x2] is set
{u1,x2} is non empty set
{u1} is non empty set
{{u1,x2},{u1}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [u1,x2] is set
z * (u1 + x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) is Relation-like [:REAL, the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[:REAL, the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the Mult of RLSStruct(# W,B,C,C #) . (z,(u1 + x2)) is set
[z,(u1 + x2)] is set
{z,(u1 + x2)} is non empty set
{z} is non empty set
{{z,(u1 + x2)},{z}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [z,(u1 + x2)] is set
z * u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (z,u1) is set
[z,u1] is set
{z,u1} is non empty set
{{z,u1},{z}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [z,u1] is set
z * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (z,x2) is set
[z,x2] is set
{z,x2} is non empty set
{{z,x2},{z}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [z,x2] is set
(z * u1) + (z * x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . ((z * u1),(z * x2)) is Element of the carrier of RLSStruct(# W,B,C,C #)
[(z * u1),(z * x2)] is set
{(z * u1),(z * x2)} is non empty set
{(z * u1)} is non empty set
{{(z * u1),(z * x2)},{(z * u1)}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [(z * u1),(z * x2)] is set
b is V31() real V33() Element of REAL
b * (u1 + x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (b,(u1 + x2)) is set
[b,(u1 + x2)] is set
{b,(u1 + x2)} is non empty set
{b} is non empty set
{{b,(u1 + x2)},{b}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [b,(u1 + x2)] is set
the Mult of V . (b,(u1 + x2)) is set
the Mult of V . [b,(u1 + x2)] is set
v1 is left_complementable right_complementable complementable Element of the carrier of V
v2 is left_complementable right_complementable complementable Element of the carrier of V
v1 + v2 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (v1,v2) is left_complementable right_complementable complementable Element of the carrier of V
[v1,v2] is set
{v1,v2} is non empty set
{v1} is non empty set
{{v1,v2},{v1}} is non empty set
the addF of V . [v1,v2] is set
b * (v1 + v2) is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (b,(v1 + v2)) is set
[b,(v1 + v2)] is set
{b,(v1 + v2)} is non empty set
{{b,(v1 + v2)},{b}} is non empty set
the Mult of V . [b,(v1 + v2)] is set
b * v1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (b,v1) is set
[b,v1] is set
{b,v1} is non empty set
{{b,v1},{b}} is non empty set
the Mult of V . [b,v1] is set
b * v2 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (b,v2) is set
[b,v2] is set
{b,v2} is non empty set
{{b,v2},{b}} is non empty set
the Mult of V . [b,v2] is set
(b * v1) + (b * v2) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((b * v1),(b * v2)) is left_complementable right_complementable complementable Element of the carrier of V
[(b * v1),(b * v2)] is set
{(b * v1),(b * v2)} is non empty set
{(b * v1)} is non empty set
{{(b * v1),(b * v2)},{(b * v1)}} is non empty set
the addF of V . [(b * v1),(b * v2)] is set
the Mult of V . (b,v1) is left_complementable right_complementable complementable Element of the carrier of V
b * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (b,x2) is set
[b,x2] is set
{b,x2} is non empty set
{{b,x2},{b}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [b,x2] is set
the addF of V . (( the Mult of V . (b,v1)),(b * x2)) is set
[( the Mult of V . (b,v1)),(b * x2)] is set
{( the Mult of V . (b,v1)),(b * x2)} is non empty set
{( the Mult of V . (b,v1))} is non empty set
{{( the Mult of V . (b,v1)),(b * x2)},{( the Mult of V . (b,v1))}} is non empty set
the addF of V . [( the Mult of V . (b,v1)),(b * x2)] is set
b * u1 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (b,u1) is set
[b,u1] is set
{b,u1} is non empty set
{{b,u1},{b}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [b,u1] is set
the addF of V . ((b * u1),(b * x2)) is set
[(b * u1),(b * x2)] is set
{(b * u1),(b * x2)} is non empty set
{(b * u1)} is non empty set
{{(b * u1),(b * x2)},{(b * u1)}} is non empty set
the addF of V . [(b * u1),(b * x2)] is set
(b * u1) + (b * x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . ((b * u1),(b * x2)) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . [(b * u1),(b * x2)] is set
z is V31() real V33() set
u1 is V31() real V33() set
z + u1 is V31() real V33() set
x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
(z + u1) * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) is Relation-like [:REAL, the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[:REAL, the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the Mult of RLSStruct(# W,B,C,C #) . ((z + u1),x2) is set
[(z + u1),x2] is set
{(z + u1),x2} is non empty set
{(z + u1)} is non empty set
{{(z + u1),x2},{(z + u1)}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [(z + u1),x2] is set
z * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (z,x2) is set
[z,x2] is set
{z,x2} is non empty set
{z} is non empty set
{{z,x2},{z}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [z,x2] is set
u1 * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (u1,x2) is set
[u1,x2] is set
{u1,x2} is non empty set
{u1} is non empty set
{{u1,x2},{u1}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [u1,x2] is set
(z * x2) + (u1 * x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) is Relation-like [: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[: the carrier of RLSStruct(# W,B,C,C #), the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the addF of RLSStruct(# W,B,C,C #) . ((z * x2),(u1 * x2)) is Element of the carrier of RLSStruct(# W,B,C,C #)
[(z * x2),(u1 * x2)] is set
{(z * x2),(u1 * x2)} is non empty set
{(z * x2)} is non empty set
{{(z * x2),(u1 * x2)},{(z * x2)}} is non empty set
the addF of RLSStruct(# W,B,C,C #) . [(z * x2),(u1 * x2)] is set
v2 is V31() real V33() Element of REAL
b is V31() real V33() Element of REAL
v2 + b is V31() real V33() Element of REAL
(v2 + b) * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . ((v2 + b),x2) is set
[(v2 + b),x2] is set
{(v2 + b),x2} is non empty set
{(v2 + b)} is non empty set
{{(v2 + b),x2},{(v2 + b)}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [(v2 + b),x2] is set
v1 is left_complementable right_complementable complementable Element of the carrier of V
(v2 + b) * v1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((v2 + b),v1) is set
[(v2 + b),v1] is set
{(v2 + b),v1} is non empty set
{{(v2 + b),v1},{(v2 + b)}} is non empty set
the Mult of V . [(v2 + b),v1] is set
v2 * v1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (v2,v1) is set
[v2,v1] is set
{v2,v1} is non empty set
{v2} is non empty set
{{v2,v1},{v2}} is non empty set
the Mult of V . [v2,v1] is set
b * v1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (b,v1) is set
[b,v1] is set
{b,v1} is non empty set
{b} is non empty set
{{b,v1},{b}} is non empty set
the Mult of V . [b,v1] is set
(v2 * v1) + (b * v1) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((v2 * v1),(b * v1)) is left_complementable right_complementable complementable Element of the carrier of V
[(v2 * v1),(b * v1)] is set
{(v2 * v1),(b * v1)} is non empty set
{(v2 * v1)} is non empty set
{{(v2 * v1),(b * v1)},{(v2 * v1)}} is non empty set
the addF of V . [(v2 * v1),(b * v1)] is set
the Mult of V . (v2,v1) is left_complementable right_complementable complementable Element of the carrier of V
b * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (b,x2) is set
[b,x2] is set
{b,x2} is non empty set
{{b,x2},{b}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [b,x2] is set
the addF of V . (( the Mult of V . (v2,v1)),(b * x2)) is set
[( the Mult of V . (v2,v1)),(b * x2)] is set
{( the Mult of V . (v2,v1)),(b * x2)} is non empty set
{( the Mult of V . (v2,v1))} is non empty set
{{( the Mult of V . (v2,v1)),(b * x2)},{( the Mult of V . (v2,v1))}} is non empty set
the addF of V . [( the Mult of V . (v2,v1)),(b * x2)] is set
v2 * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (v2,x2) is set
[v2,x2] is set
{v2,x2} is non empty set
{{v2,x2},{v2}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [v2,x2] is set
the addF of V . ((v2 * x2),(b * x2)) is set
[(v2 * x2),(b * x2)] is set
{(v2 * x2),(b * x2)} is non empty set
{(v2 * x2)} is non empty set
{{(v2 * x2),(b * x2)},{(v2 * x2)}} is non empty set
the addF of V . [(v2 * x2),(b * x2)] is set
(v2 * x2) + (b * x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . ((v2 * x2),(b * x2)) is Element of the carrier of RLSStruct(# W,B,C,C #)
the addF of RLSStruct(# W,B,C,C #) . [(v2 * x2),(b * x2)] is set
z is V31() real V33() set
u1 is V31() real V33() set
z * u1 is V31() real V33() set
x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
(z * u1) * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) is Relation-like [:REAL, the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[:REAL, the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the Mult of RLSStruct(# W,B,C,C #) . ((z * u1),x2) is set
[(z * u1),x2] is set
{(z * u1),x2} is non empty set
{(z * u1)} is non empty set
{{(z * u1),x2},{(z * u1)}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [(z * u1),x2] is set
u1 * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (u1,x2) is set
[u1,x2] is set
{u1,x2} is non empty set
{u1} is non empty set
{{u1,x2},{u1}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [u1,x2] is set
z * (u1 * x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (z,(u1 * x2)) is set
[z,(u1 * x2)] is set
{z,(u1 * x2)} is non empty set
{z} is non empty set
{{z,(u1 * x2)},{z}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [z,(u1 * x2)] is set
v2 is V31() real V33() Element of REAL
b is V31() real V33() Element of REAL
v2 * b is V31() real V33() Element of REAL
(v2 * b) * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . ((v2 * b),x2) is set
[(v2 * b),x2] is set
{(v2 * b),x2} is non empty set
{(v2 * b)} is non empty set
{{(v2 * b),x2},{(v2 * b)}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [(v2 * b),x2] is set
v1 is left_complementable right_complementable complementable Element of the carrier of V
(v2 * b) * v1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((v2 * b),v1) is set
[(v2 * b),v1] is set
{(v2 * b),v1} is non empty set
{{(v2 * b),v1},{(v2 * b)}} is non empty set
the Mult of V . [(v2 * b),v1] is set
b * v1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (b,v1) is set
[b,v1] is set
{b,v1} is non empty set
{b} is non empty set
{{b,v1},{b}} is non empty set
the Mult of V . [b,v1] is set
v2 * (b * v1) is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (v2,(b * v1)) is set
[v2,(b * v1)] is set
{v2,(b * v1)} is non empty set
{v2} is non empty set
{{v2,(b * v1)},{v2}} is non empty set
the Mult of V . [v2,(b * v1)] is set
b * x2 is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (b,x2) is set
[b,x2] is set
{b,x2} is non empty set
{{b,x2},{b}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [b,x2] is set
the Mult of V . (v2,(b * x2)) is set
[v2,(b * x2)] is set
{v2,(b * x2)} is non empty set
{{v2,(b * x2)},{v2}} is non empty set
the Mult of V . [v2,(b * x2)] is set
v2 * (b * x2) is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) . (v2,(b * x2)) is set
the Mult of RLSStruct(# W,B,C,C #) . [v2,(b * x2)] is set
z is Element of the carrier of RLSStruct(# W,B,C,C #)
1 * z is Element of the carrier of RLSStruct(# W,B,C,C #)
the Mult of RLSStruct(# W,B,C,C #) is Relation-like [:REAL, the carrier of RLSStruct(# W,B,C,C #):] -defined the carrier of RLSStruct(# W,B,C,C #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #)) Element of bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):]
[:REAL, the carrier of RLSStruct(# W,B,C,C #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# W,B,C,C #):], the carrier of RLSStruct(# W,B,C,C #):] is non empty set
the Mult of RLSStruct(# W,B,C,C #) . (1,z) is set
[1,z] is set
{1,z} is non empty set
{1} is non empty set
{{1,z},{1}} is non empty set
the Mult of RLSStruct(# W,B,C,C #) . [1,z] is set
u1 is left_complementable right_complementable complementable Element of the carrier of V
1 * u1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (1,u1) is set
[1,u1] is set
{1,u1} is non empty set
{{1,u1},{1}} is non empty set
the Mult of V . [1,u1] is set
0. RLSStruct(# W,B,C,C #) is V55( RLSStruct(# W,B,C,C #)) Element of the carrier of RLSStruct(# W,B,C,C #)
the ZeroF of RLSStruct(# W,B,C,C #) is Element of the carrier of RLSStruct(# W,B,C,C #)
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V | [:REAL, the carrier of V:] is Relation-like Function-like set
V is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of u is non empty set
the carrier of V is non empty set
the addF of u is Relation-like [: the carrier of u, the carrier of u:] -defined the carrier of u -valued 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 non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] 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 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 Mult of u is Relation-like [:REAL, the carrier of u:] -defined the carrier of u -valued Function-like V18([:REAL, the carrier of u:], the carrier of u) Element of bool [:[:REAL, the carrier of u:], the carrier of u:]
[:REAL, the carrier of u:] is non empty set
[:[:REAL, the carrier of u:], the carrier of u:] is non empty set
bool [:[:REAL, the carrier of u:], the carrier of u:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V | [:REAL, the carrier of u:] is Relation-like Function-like set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
the Mult of u | [:REAL, the carrier of V:] is Relation-like Function-like set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
the carrier of u is non empty set
the carrier of W is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
0. W is V55(W) left_complementable right_complementable complementable Element of the carrier of W
the ZeroF of W is left_complementable right_complementable complementable Element of the carrier of W
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 [: the carrier of W, the carrier of W:] -defined the carrier of W -valued 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 non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is 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 Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of W is Relation-like [:REAL, the carrier of W:] -defined the carrier of W -valued Function-like V18([:REAL, the carrier of W:], the carrier of W) Element of bool [:[:REAL, the carrier of W:], the carrier of W:]
[:REAL, the carrier of W:] is non empty set
[:[:REAL, the carrier of W:], the carrier of W:] is non empty set
bool [:[:REAL, the carrier of W:], the carrier of W:] is non empty set
the Mult of W | [:REAL, the carrier of V:] is Relation-like Function-like set
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
the addF of u is Relation-like [: the carrier of u, the carrier of u:] -defined the carrier of u -valued 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 non empty set
[:[: the carrier of u, the carrier of u:], the carrier of u:] is 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 Mult of u is Relation-like [:REAL, the carrier of u:] -defined the carrier of u -valued Function-like V18([:REAL, the carrier of u:], the carrier of u) Element of bool [:[:REAL, the carrier of u:], the carrier of u:]
[:REAL, the carrier of u:] is non empty set
[:[:REAL, the carrier of u:], the carrier of u:] is non empty set
bool [:[:REAL, the carrier of u:], the carrier of u:] is non empty set
the Mult of u | [:REAL, the carrier of V:] is Relation-like Function-like set
the Mult of W | [:REAL, the carrier of u:] is Relation-like Function-like set
( the Mult of W | [:REAL, the carrier of u:]) | [:REAL, the carrier of V:] is Relation-like Function-like set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
[: the carrier of u, the carrier of u:] is non empty set
[: the carrier of W, the carrier of W:] is non empty set
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the ZeroF of u is left_complementable right_complementable complementable Element of the carrier of u
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
0. W is V55(W) left_complementable right_complementable complementable Element of the carrier of W
the ZeroF of W is left_complementable right_complementable complementable Element of the carrier of W
the addF of u is Relation-like [: the carrier of u, the carrier of u:] -defined the carrier of u -valued 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:], the carrier of u:] is non empty set
bool [:[: the carrier of u, the carrier of u:], the carrier of u:] is non empty set
the addF of W is Relation-like [: the carrier of W, the carrier of W:] -defined the carrier of W -valued 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:], the carrier of W:] is 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 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 Mult of u is Relation-like [:REAL, the carrier of u:] -defined the carrier of u -valued Function-like V18([:REAL, the carrier of u:], the carrier of u) Element of bool [:[:REAL, the carrier of u:], the carrier of u:]
[:REAL, the carrier of u:] is non empty set
[:[:REAL, the carrier of u:], the carrier of u:] is non empty set
bool [:[:REAL, the carrier of u:], the carrier of u:] is non empty set
the Mult of W is Relation-like [:REAL, the carrier of W:] -defined the carrier of W -valued Function-like V18([:REAL, the carrier of W:], the carrier of W) Element of bool [:[:REAL, the carrier of W:], the carrier of W:]
[:REAL, the carrier of W:] is non empty set
[:[:REAL, the carrier of W:], the carrier of W:] is non empty set
bool [:[:REAL, the carrier of W:], the carrier of W:] is non empty set
the Mult of W | [:REAL, the carrier of u:] is Relation-like Function-like 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 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 Mult of V | [:REAL, the carrier of u:] is Relation-like Function-like set
the Mult of V | [:REAL, the carrier of W:] is Relation-like Function-like set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
the carrier of W is non empty set
B is set
C is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
u is Element of bool the carrier of V
the addF of V || u is Relation-like Function-like set
[:u,u:] is set
the addF of V | [:u,u:] is Relation-like Function-like set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
[:REAL,u:] is set
the Mult of V | [:REAL,u:] is Relation-like Function-like set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
RLSStruct(# the carrier of V,(0. V), the addF of V, the Mult of V #) is non empty strict RLSStruct
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
W is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
the carrier of W is non empty set
B is set
C is left_complementable right_complementable complementable Element of the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
V is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
u is Element of bool the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
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
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
[:REAL,u:] is set
the Mult of V | [:REAL,u:] is Relation-like Function-like set
dom the Mult of V is Relation-like set
dom ( the Mult of V | [:REAL,u:]) is set
[:REAL, the carrier of V:] /\ [:REAL,u:] is set
W is non empty set
[:REAL,W:] is non empty set
C is set
[1,C] is set
{1,C} is non empty set
{1} is non empty set
{{1,C},{1}} is non empty set
( the Mult of V | [:REAL,u:]) . [1,C] is set
c7 is left_complementable right_complementable complementable Element of the carrier of V
1 * c7 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (1,c7) is set
[1,c7] is set
{1,c7} is non empty set
{{1,c7},{1}} is non empty set
the Mult of V . [1,c7] is set
c7 is set
( the Mult of V | [:REAL,u:]) . c7 is set
x is set
x is set
[x,x] is set
{x,x} is non empty set
{x} is non empty set
{{x,x},{x}} is non empty set
u1 is left_complementable right_complementable complementable Element of the carrier of V
z is V31() real V33() Element of REAL
z * u1 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (z,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
the Mult of V . [z,u1] is set
rng ( the Mult of V | [:REAL,u:]) is set
[:[:REAL,W:],W:] is non empty set
bool [:[:REAL,W:],W:] is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 is Relation-like Function-like set
[:u,u:] is set
the addF of V | [:u,u:] is Relation-like Function-like set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
dom the addF of V is Relation-like set
dom ( the addF of V || u) is set
[:u,u:] is Relation-like the carrier of V -defined the carrier of V -valued Element of bool [: the carrier of V, the carrier of V:]
bool [: the carrier of V, the carrier of V:] is non empty set
[: the carrier of V, the carrier of V:] /\ [:u,u:] is Relation-like the carrier of V -defined the carrier of V -valued Element of bool [: the carrier of V, the carrier of V:]
[:W,W:] is non empty set
x is set
x is Element of W
[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 || u) . [x,x] is set
u1 is left_complementable right_complementable complementable Element of the carrier of V
z is left_complementable right_complementable complementable Element of the carrier of V
u1 + z is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u1,z) is left_complementable right_complementable complementable Element of the carrier of V
[u1,z] is set
{u1,z} is non empty set
{u1} is non empty set
{{u1,z},{u1}} is non empty set
the addF of V . [u1,z] is set
z is set
( the addF of V || u) . z is set
u1 is set
x2 is set
[u1,x2] is set
{u1,x2} is non empty set
{u1} is non empty set
{{u1,x2},{u1}} is non empty set
v1 is left_complementable right_complementable complementable Element of the carrier of V
v2 is left_complementable right_complementable complementable Element of the carrier of V
v1 + v2 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (v1,v2) is left_complementable right_complementable complementable Element of the carrier of V
[v1,v2] is set
{v1,v2} is non empty set
{v1} is non empty set
{{v1,v2},{v1}} is non empty set
the addF of V . [v1,v2] is set
rng ( the addF of V || u) is set
[:[:W,W:],W:] is non empty set
bool [:[:W,W:],W:] is non empty set
x is Element of W
x is Relation-like [:W,W:] -defined W -valued Function-like V18([:W,W:],W) Element of bool [:[:W,W:],W:]
C is Relation-like [:REAL,W:] -defined W -valued Function-like V18([:REAL,W:],W) Element of bool [:[:REAL,W:],W:]
RLSStruct(# W,x,x,C #) is non empty strict RLSStruct
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable 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 left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of W is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict RLSStruct
the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty set
W is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
W + B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,B) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,B] is set
C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
(W + B) + C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((W + B),C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(W + B),C] is set
B + C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (B,C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [B,C] is set
W + (B + C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,(B + C)) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,(B + C)] is set
C is left_complementable right_complementable complementable Element of the carrier of V
c7 is left_complementable right_complementable complementable Element of the carrier of V
C + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,c7) is left_complementable right_complementable complementable Element of the carrier of V
[C,c7] is set
{C,c7} is non empty set
{C} is non empty set
{{C,c7},{C}} is non empty set
the addF of V . [C,c7] is set
x is left_complementable right_complementable complementable Element of the carrier of V
(C + c7) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((C + c7),x) is left_complementable right_complementable complementable Element of the carrier of V
[(C + c7),x] is set
{(C + c7),x} is non empty set
{(C + c7)} is non empty set
{{(C + c7),x},{(C + c7)}} is non empty set
the addF of V . [(C + c7),x] is set
c7 + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,x) is left_complementable right_complementable complementable Element of the carrier of V
[c7,x] is set
{c7,x} is non empty set
{c7} is non empty set
{{c7,x},{c7}} is non empty set
the addF of V . [c7,x] is set
C + (c7 + x) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(c7 + x)) is left_complementable right_complementable complementable Element of the carrier of V
[C,(c7 + x)] is set
{C,(c7 + x)} is non empty set
{{C,(c7 + x)},{C}} is non empty set
the addF of V . [C,(c7 + x)] is set
0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is V55( RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the ZeroF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
W is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
W + (0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,(0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
[W,(0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))] is set
{W,(0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))} is non empty set
{W} is non empty set
{{W,(0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))},{W}} is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,(0. RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #))] is set
B is left_complementable right_complementable complementable Element of the carrier of V
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
B + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,(0. V)) is left_complementable right_complementable 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
B is left_complementable right_complementable complementable Element of the carrier of V
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
B + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,C) is left_complementable right_complementable 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
W + C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,C] is set
W is V31() real V33() set
B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
B + C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (B,C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [B,C] is set
W * (B + C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,(B + C)) is set
[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 Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,(B + C)] is set
W * B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,B) is set
[W,B] is set
{W,B} is non empty set
{{W,B},{W}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,B] is set
W * C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,C) is set
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,C] is set
(W * B) + (W * C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((W * B),(W * C)) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(W * B),(W * C)] is set
C is left_complementable right_complementable complementable Element of the carrier of V
c7 is left_complementable right_complementable complementable Element of the carrier of V
C + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,c7) is left_complementable right_complementable complementable Element of the carrier of V
[C,c7] is set
{C,c7} is non empty set
{C} is non empty set
{{C,c7},{C}} is non empty set
the addF of V . [C,c7] is set
W * (C + c7) is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (W,(C + c7)) is set
[W,(C + c7)] is set
{W,(C + c7)} is non empty set
{{W,(C + c7)},{W}} is non empty set
the Mult of V . [W,(C + c7)] is set
W * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (W,C) is set
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the Mult of V . [W,C] is set
W * c7 is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (W,c7) is set
[W,c7] is set
{W,c7} is non empty set
{{W,c7},{W}} is non empty set
the Mult of V . [W,c7] is set
(W * C) + (W * c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W * C),(W * c7)) is left_complementable right_complementable complementable Element of the carrier of V
[(W * C),(W * c7)] is set
{(W * C),(W * c7)} is non empty set
{(W * C)} is non empty set
{{(W * C),(W * c7)},{(W * C)}} is non empty set
the addF of V . [(W * C),(W * c7)] is set
W is V31() real V33() set
B is V31() real V33() set
W * B is V31() real V33() set
C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
(W * B) * C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((W * B),C) is set
[(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 Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(W * B),C] is set
B * C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (B,C) is set
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [B,C] is set
W * (B * C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,(B * C)) is set
[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 Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,(B * C)] is set
C is left_complementable right_complementable complementable Element of the carrier of V
(W * B) * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((W * B),C) is set
[(W * B),C] is set
{(W * B),C} is non empty set
{{(W * B),C},{(W * B)}} is non empty set
the Mult of V . [(W * B),C] is set
B * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (B,C) is set
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the Mult of V . [B,C] is set
W * (B * C) is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (W,(B * C)) is set
[W,(B * C)] is set
{W,(B * C)} is non empty set
{{W,(B * C)},{W}} is non empty set
the Mult of V . [W,(B * C)] is set
W is V31() real V33() set
B is V31() real V33() set
W + B is V31() real V33() set
C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
(W + B) * C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((W + B),C) is set
[(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 Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(W + B),C] is set
W * C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,C) is set
[W,C] is set
{W,C} is non empty set
{W} is non empty set
{{W,C},{W}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,C] is set
B * C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (B,C) is set
[B,C] is set
{B,C} is non empty set
{B} is non empty set
{{B,C},{B}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [B,C] is set
(W * C) + (B * C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . ((W * C),(B * C)) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [(W * C),(B * C)] is set
C is left_complementable right_complementable complementable Element of the carrier of V
(W + B) * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((W + B),C) is set
[(W + B),C] is set
{(W + B),C} is non empty set
{{(W + B),C},{(W + B)}} is non empty set
the Mult of V . [(W + B),C] is set
W * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (W,C) is set
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the Mult of V . [W,C] is set
B * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (B,C) is set
[B,C] is set
{B,C} is non empty set
{{B,C},{B}} is non empty set
the Mult of V . [B,C] is set
(W * C) + (B * C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W * C),(B * C)) is left_complementable right_complementable 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
B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
C is left_complementable right_complementable complementable Element of the carrier of V
C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
c7 is left_complementable right_complementable complementable Element of the carrier of V
B + C is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (B,C) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [B,C] is set
C + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,c7) is left_complementable right_complementable complementable Element of the carrier of V
[C,c7] is set
{C,c7} is non empty set
{C} is non empty set
{{C,c7},{C}} is non empty set
the addF of V . [C,c7] is set
W is V31() real V33() Element of REAL
W * B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,B) is set
[W,B] is set
{W,B} is non empty set
{W} is non empty set
{{W,B},{W}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,B] is set
W * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (W,C) is set
[W,C] is set
{W,C} is non empty set
{{W,C},{W}} is non empty set
the Mult of V . [W,C] is set
W is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
W + B is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[: the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #), the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (W,B) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [W,B] is set
B + W is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the addF of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (B,W) is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [B,W] is set
C is left_complementable right_complementable complementable Element of the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
C + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,C) is left_complementable right_complementable 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 RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
1 * W is Element of the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is Relation-like [:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] -defined the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) -valued Function-like V18([:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #)) Element of bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):]
[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
[:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
bool [:[:REAL, the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):], the carrier of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #):] is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . (1,W) is set
[1,W] is set
{1,W} is non empty set
{1} is non empty set
{{1,W},{1}} is non empty set
the Mult of RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) . [1,W] is set
B is left_complementable right_complementable complementable Element of the carrier of V
1 * B is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (1,B) is set
[1,B] is set
{1,B} is non empty set
{{1,B},{1}} is non empty set
the Mult of V . [1,B] is set
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the Mult of W is Relation-like [:REAL, the carrier of W:] -defined the carrier of W -valued Function-like V18([:REAL, the carrier of W:], the carrier of W) Element of bool [:[:REAL, the carrier of W:], the carrier of W:]
the carrier of W is non empty set
[:REAL, the carrier of W:] is non empty set
[:[:REAL, the carrier of W:], the carrier of W:] is non empty set
bool [:[:REAL, the carrier of W:], the carrier of W:] is non empty set
the Mult of V | [:REAL, the carrier of W:] is Relation-like Function-like set
0. W is V55(W) left_complementable right_complementable complementable Element of the carrier of W
the ZeroF of W is left_complementable right_complementable complementable Element of the carrier of W
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the addF of W is Relation-like [: the carrier of W, the carrier of W:] -defined the carrier of W -valued 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 non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(u) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (u)
the carrier of (u) is non empty set
the carrier of u is non empty set
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the ZeroF of u is left_complementable right_complementable 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 (V) is non empty set
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(u) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (u)
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(W) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (W)
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(u) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (u)
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of (V) is non empty set
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable 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
the carrier of u is non empty set
0. u is V55(u) left_complementable right_complementable complementable Element of the carrier of u
the ZeroF of u is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(u) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (u)
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(W) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (W)
V is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict RLSStruct
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
{ (u + b1) where b1 is left_complementable right_complementable 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
c7 is set
x is left_complementable right_complementable complementable Element of the carrier of V
u + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
c7 is set
x is left_complementable right_complementable complementable Element of the carrier of V
u + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(0. V) + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(0. V) + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is Element of bool the carrier of V
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(V,(0. V),u) is Element of bool the carrier of V
{ ((0. V) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in u } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
B is left_complementable right_complementable complementable Element of the carrier of V
u + B is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
u - u is left_complementable right_complementable complementable Element of the carrier of V
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in u } is set
the carrier of u is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
u is left_complementable right_complementable complementable Element of the carrier of V
(V,u,(V)) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in (V) } is set
{u} is non empty Element of bool the carrier of V
W is set
B is left_complementable right_complementable complementable Element of the carrier of V
u + B is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 (V) is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
the carrier of W is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of W
C is left_complementable right_complementable complementable Element of the carrier of W
C - C is left_complementable right_complementable complementable Element of the carrier of W
- C is left_complementable right_complementable complementable Element of the carrier of W
C + (- C) is left_complementable right_complementable complementable Element of the carrier of W
the addF of W is Relation-like [: the carrier of W, the carrier of W:] -defined the carrier of W -valued 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 non empty set
[:[: the carrier of W, the carrier of W:], the carrier of W:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of W
the addF of W . (C,(C - C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of W
the addF of W . (C,C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of W
(C + C) + (- C) is left_complementable right_complementable complementable Element of the carrier of W
the addF of W . ((C + C),(- C)) is left_complementable right_complementable complementable Element of the carrier of W
[(C + C),(- C)] is set
{(C + C),(- C)} is non empty set
{(C + C)} is non empty set
{{(C + C),(- C)},{(C + C)}} is non empty set
the addF of W . [(C + C),(- C)] is set
C - C is left_complementable right_complementable complementable Element of the carrier of W
C + (- C) is left_complementable right_complementable complementable Element of the carrier of W
the addF of W . (C,(- C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of W
the addF of W . (C,(C - C)) is left_complementable right_complementable 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 V55(W) left_complementable right_complementable complementable Element of the carrier of W
the ZeroF of W is left_complementable right_complementable complementable Element of the carrier of W
C + (0. W) is left_complementable right_complementable complementable Element of the carrier of W
the addF of W . (C,(0. W)) is left_complementable right_complementable 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
c7 is left_complementable right_complementable complementable Element of the carrier of V
x is left_complementable right_complementable complementable Element of the carrier of V
c7 - x is left_complementable right_complementable complementable Element of the carrier of V
- x is left_complementable right_complementable complementable Element of the carrier of V
c7 + (- x) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(- x)) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(- x)] is set
{c7,(- x)} is non empty set
{c7} is non empty set
{{c7,(- x)},{c7}} is non empty set
the addF of V . [c7,(- x)] is set
x + (c7 - x) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (x,(c7 - x)) is left_complementable right_complementable complementable Element of the carrier of V
[x,(c7 - x)] is set
{x,(c7 - x)} is non empty set
{x} is non empty set
{{x,(c7 - x)},{x}} is non empty set
the addF of V . [x,(c7 - x)] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict RLSStruct
u is left_complementable right_complementable complementable Element of the carrier of V
(V,u,(V)) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (u + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in (V) } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
the carrier of W is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of B is non empty set
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
u is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
the carrier of W is non empty set
C is left_complementable right_complementable complementable Element of the carrier of B
C is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (B)
(B,C,C) is Element of bool the carrier of B
bool the carrier of B is non empty set
{ (C + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of B : b1 in C } is set
the carrier of C is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is V31() real V33() Element of REAL
W * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,u) is set
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the Mult of V . [W,u] is set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(V,(W * u),B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((W * u) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
the carrier of B is non empty set
C is set
C is left_complementable right_complementable complementable Element of the carrier of V
(W * u) + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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),C) is left_complementable right_complementable 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
C is set
C is left_complementable right_complementable complementable Element of the carrier of V
C - (W * u) is left_complementable right_complementable complementable Element of the carrier of V
- (W * u) is left_complementable right_complementable complementable Element of the carrier of V
C + (- (W * u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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,(- (W * u))) is left_complementable right_complementable 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
(W * u) + (C - (W * u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W * u),(C - (W * u))) is left_complementable right_complementable complementable Element of the carrier of V
[(W * u),(C - (W * u))] is set
{(W * u),(C - (W * u))} is non empty set
{(W * u)} is non empty set
{{(W * u),(C - (W * u))},{(W * u)}} is non empty set
the addF of V . [(W * u),(C - (W * u))] is set
C + (W * u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(W * u)) is left_complementable right_complementable complementable Element of the carrier of V
[C,(W * u)] is set
{C,(W * u)} is non empty set
{{C,(W * u)},{C}} is non empty set
the addF of V . [C,(W * u)] is set
(C + (W * u)) - (W * u) is left_complementable right_complementable complementable Element of the carrier of V
(C + (W * u)) + (- (W * u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((C + (W * u)),(- (W * u))) is left_complementable right_complementable complementable Element of the carrier of V
[(C + (W * u)),(- (W * u))] is set
{(C + (W * u)),(- (W * u))} is non empty set
{(C + (W * u))} is non empty set
{{(C + (W * u)),(- (W * u))},{(C + (W * u))}} is non empty set
the addF of V . [(C + (W * u)),(- (W * u))] is set
(W * u) - (W * u) is left_complementable right_complementable complementable Element of the carrier of V
(W * u) + (- (W * u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W * u),(- (W * u))) is left_complementable right_complementable complementable Element of the carrier of V
[(W * u),(- (W * u))] is set
{(W * u),(- (W * u))} is non empty set
{{(W * u),(- (W * u))},{(W * u)}} is non empty set
the addF of V . [(W * u),(- (W * u))] is set
C + ((W * u) - (W * u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,((W * u) - (W * u))) is left_complementable right_complementable complementable Element of the carrier of V
[C,((W * u) - (W * u))] is set
{C,((W * u) - (W * u))} is non empty set
{{C,((W * u) - (W * u))},{C}} is non empty set
the addF of V . [C,((W * u) - (W * u))] is set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
C + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(0. V)) is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is V31() real V33() Element of REAL
W * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,u) is set
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the Mult of V . [W,u] is set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(V,(W * u),B) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((W * u) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
the carrier of B is non empty set
1 * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (1,u) is set
[1,u] is set
{1,u} is non empty set
{1} is non empty set
{{1,u},{1}} is non empty set
the Mult of V . [1,u] is set
W " is V31() real V33() Element of REAL
(W ") * W is V31() real V33() Element of REAL
((W ") * W) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (((W ") * W),u) is set
[((W ") * W),u] is set
{((W ") * W),u} is non empty set
{((W ") * W)} is non empty set
{{((W ") * W),u},{((W ") * W)}} is non empty set
the Mult of V . [((W ") * W),u] is set
(W ") * (W * u) is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((W "),(W * u)) is set
[(W "),(W * u)] is set
{(W "),(W * u)} is non empty set
{(W ")} is non empty set
{{(W "),(W * u)},{(W ")}} is non empty set
the Mult of V . [(W "),(W * u)] is set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(W * u) + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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),(0. V)) is left_complementable right_complementable complementable Element of the carrier of V
[(W * u),(0. V)] is set
{(W * u),(0. V)} is non empty set
{(W * u)} is non empty set
{{(W * u),(0. V)},{(W * u)}} is non empty set
the addF of V . [(W * u),(0. V)] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
the carrier of W is non empty set
(- 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . ((- 1),u) is set
[(- 1),u] is set
{(- 1),u} is non empty set
{(- 1)} is non empty set
{{(- 1),u},{(- 1)}} is non empty set
the Mult of V . [(- 1),u] is set
(V,((- 1) * u),W) is Element of bool the carrier of V
{ (((- 1) * u) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
W + u is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,(W + u),B) is Element of bool the carrier of V
{ ((W + u) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
C + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W + u),(C - u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(C - u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(u + (C - u))) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,u) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(C + u) + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((C + u),(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,((C + u) - u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(u - u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(C + (u - u))) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
C + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(0. V)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(C + (0. V))) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(W + u) + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W + u),C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(u + C)) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
W + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(0. V)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(W + u) + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W + u),C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,C) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(u + C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
W - u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,(W - u),B) is Element of bool the carrier of V
{ ((W - u) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
- (- u) is left_complementable right_complementable complementable Element of the carrier of V
W + (- u) is left_complementable right_complementable complementable Element of the carrier of V
(V,(W + (- u)),B) is Element of bool the carrier of V
{ ((W + (- u)) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,u,B) is Element of bool the carrier of V
{ (u + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
c7 is left_complementable right_complementable complementable Element of the carrier of V
W + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,c7) is left_complementable right_complementable complementable Element of the carrier of V
[W,c7] is set
{W,c7} is non empty set
{{W,c7},{W}} is non empty set
the addF of V . [W,c7] is set
u - C is left_complementable right_complementable complementable Element of the carrier of V
- C is left_complementable right_complementable complementable Element of the carrier of V
u + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
C + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(- C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(C - C)) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
W + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(0. V)) is left_complementable right_complementable 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
c7 + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(- C)] is set
{c7,(- C)} is non empty set
{c7} is non empty set
{{c7,(- C)},{c7}} is non empty set
the addF of V . [c7,(- C)] is set
u + (c7 + (- C)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(c7 + (- C))) is left_complementable right_complementable complementable Element of the carrier of V
[u,(c7 + (- C))] is set
{u,(c7 + (- C))} is non empty set
{{u,(c7 + (- C))},{u}} is non empty set
the addF of V . [u,(c7 + (- C))] is set
c7 - C is left_complementable right_complementable complementable Element of the carrier of V
c7 + (- C) is left_complementable right_complementable complementable Element of the carrier of V
u + (c7 - C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(c7 - C)) is left_complementable right_complementable complementable Element of the carrier of V
[u,(c7 - C)] is set
{u,(c7 - C)} is non empty set
{{u,(c7 - C)},{u}} is non empty set
the addF of V . [u,(c7 - C)] is set
C is set
c7 is left_complementable right_complementable complementable Element of the carrier of V
u + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,c7) is left_complementable right_complementable complementable Element of the carrier of V
[u,c7] is set
{u,c7} is non empty set
{u} is non empty set
{{u,c7},{u}} is non empty set
the addF of V . [u,c7] is set
C + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,c7) is left_complementable right_complementable complementable Element of the carrier of V
[C,c7] is set
{C,c7} is non empty set
{C} is non empty set
{{C,c7},{C}} is non empty set
the addF of V . [C,c7] is set
W + (C + c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(C + c7)) is left_complementable right_complementable complementable Element of the carrier of V
[W,(C + c7)] is set
{W,(C + c7)} is non empty set
{{W,(C + c7)},{W}} is non empty set
the addF of V . [W,(C + c7)] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
(V,(- u),W) is Element of bool the carrier of V
{ ((- u) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
B is left_complementable right_complementable complementable Element of the carrier of V
(- u) + B is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u - ((- u) + B) is left_complementable right_complementable complementable Element of the carrier of V
- ((- u) + B) is left_complementable right_complementable complementable Element of the carrier of V
u + (- ((- u) + B)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- ((- u) + B))) is left_complementable right_complementable complementable Element of the carrier of V
[u,(- ((- u) + B))] is set
{u,(- ((- u) + B))} is non empty set
{u} is non empty set
{{u,(- ((- u) + B))},{u}} is non empty set
the addF of V . [u,(- ((- u) + B))] is set
u - (- u) is left_complementable right_complementable complementable Element of the carrier of V
- (- u) is left_complementable right_complementable complementable Element of the carrier of V
u + (- (- u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- (- u))) is left_complementable right_complementable 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)) - B is left_complementable right_complementable complementable Element of the carrier of V
- B is left_complementable right_complementable complementable Element of the carrier of V
(u - (- u)) + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u - (- u)),(- B)) is left_complementable right_complementable complementable Element of the carrier of V
[(u - (- u)),(- B)] is set
{(u - (- u)),(- B)} is non empty set
{(u - (- u))} is non empty set
{{(u - (- u)),(- B)},{(u - (- u))}} is non empty set
the addF of V . [(u - (- u)),(- B)] is set
u + u is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,u) is left_complementable right_complementable 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) - B is left_complementable right_complementable complementable Element of the carrier of V
(u + u) + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u + u),(- B)) is left_complementable right_complementable complementable Element of the carrier of V
[(u + u),(- B)] is set
{(u + u),(- B)} is non empty set
{(u + u)} is non empty set
{{(u + u),(- B)},{(u + u)}} is non empty set
the addF of V . [(u + u),(- B)] is set
1 * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (1,u) is set
[1,u] is set
{1,u} is non empty set
{1} is non empty set
{{1,u},{1}} is non empty set
the Mult of V . [1,u] is set
(1 * u) + u is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((1 * u),u) is left_complementable right_complementable complementable Element of the carrier of V
[(1 * u),u] is set
{(1 * u),u} is non empty set
{(1 * u)} is non empty set
{{(1 * u),u},{(1 * u)}} is non empty set
the addF of V . [(1 * u),u] is set
((1 * u) + u) - B is left_complementable right_complementable complementable Element of the carrier of V
((1 * u) + u) + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (((1 * u) + u),(- B)) is left_complementable right_complementable complementable Element of the carrier of V
[((1 * u) + u),(- B)] is set
{((1 * u) + u),(- B)} is non empty set
{((1 * u) + u)} is non empty set
{{((1 * u) + u),(- B)},{((1 * u) + u)}} is non empty set
the addF of V . [((1 * u) + u),(- B)] is set
(1 * u) + (1 * u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((1 * u),(1 * u)) is left_complementable right_complementable complementable Element of the carrier of V
[(1 * u),(1 * u)] is set
{(1 * u),(1 * u)} is non empty set
{{(1 * u),(1 * u)},{(1 * u)}} is non empty set
the addF of V . [(1 * u),(1 * u)] is set
((1 * u) + (1 * u)) - B is left_complementable right_complementable complementable Element of the carrier of V
((1 * u) + (1 * u)) + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (((1 * u) + (1 * u)),(- B)) is left_complementable right_complementable complementable Element of the carrier of V
[((1 * u) + (1 * u)),(- B)] is set
{((1 * u) + (1 * u)),(- B)} is non empty set
{((1 * u) + (1 * u))} is non empty set
{{((1 * u) + (1 * u)),(- B)},{((1 * u) + (1 * u))}} is non empty set
the addF of V . [((1 * u) + (1 * u)),(- B)] is set
1 + 1 is V31() real V33() Element of REAL
(1 + 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((1 + 1),u) is set
[(1 + 1),u] is set
{(1 + 1),u} is non empty set
{(1 + 1)} is non empty set
{{(1 + 1),u},{(1 + 1)}} is non empty set
the Mult of V . [(1 + 1),u] is set
((1 + 1) * u) - B is left_complementable right_complementable complementable Element of the carrier of V
((1 + 1) * u) + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (((1 + 1) * u),(- B)) is left_complementable right_complementable complementable Element of the carrier of V
[((1 + 1) * u),(- B)] is set
{((1 + 1) * u),(- B)} is non empty set
{((1 + 1) * u)} is non empty set
{{((1 + 1) * u),(- B)},{((1 + 1) * u)}} is non empty set
the addF of V . [((1 + 1) * u),(- B)] is set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V31() real V33() Element of NAT
2 * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (2,u) is set
[2,u] is set
{2,u} is non empty set
{2} is non empty set
{{2,u},{2}} is non empty set
the Mult of V . [2,u] is set
(2 * u) - B is left_complementable right_complementable complementable Element of the carrier of V
(2 * u) + (- B) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((2 * u),(- B)) is left_complementable right_complementable complementable Element of the carrier of V
[(2 * u),(- B)] is set
{(2 * u),(- B)} is non empty set
{(2 * u)} is non empty set
{{(2 * u),(- B)},{(2 * u)}} is non empty set
the addF of V . [(2 * u),(- B)] is set
2 " is V31() real V33() Element of REAL
(2 ") * (2 * u) is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((2 "),(2 * u)) is set
[(2 "),(2 * u)] is set
{(2 "),(2 * u)} is non empty set
{(2 ")} is non empty set
{{(2 "),(2 * u)},{(2 ")}} is non empty set
the Mult of V . [(2 "),(2 * u)] is set
(2 ") * B is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((2 "),B) is set
[(2 "),B] is set
{(2 "),B} is non empty set
{{(2 "),B},{(2 ")}} is non empty set
the Mult of V . [(2 "),B] is set
(2 ") * 2 is V31() real V33() Element of REAL
((2 ") * 2) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (((2 ") * 2),u) is set
[((2 ") * 2),u] is set
{((2 ") * 2),u} is non empty set
{((2 ") * 2)} is non empty set
{{((2 ") * 2),u},{((2 ") * 2)}} is non empty set
the Mult of V . [((2 ") * 2),u] is set
the carrier of W is non empty set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is left_complementable right_complementable complementable Element of the carrier of V
C is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in C } is set
(V,B,C) is Element of bool the carrier of V
{ (B + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in C } is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
c7 is left_complementable right_complementable complementable Element of the carrier of V
B + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,c7) is left_complementable right_complementable complementable Element of the carrier of V
[B,c7] is set
{B,c7} is non empty set
{B} is non empty set
{{B,c7},{B}} is non empty set
the addF of V . [B,c7] is set
x is set
x is left_complementable right_complementable complementable Element of the carrier of V
W + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,x) is left_complementable right_complementable 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
c7 - C is left_complementable right_complementable complementable Element of the carrier of V
- C is left_complementable right_complementable complementable Element of the carrier of V
c7 + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(- C)] is set
{c7,(- C)} is non empty set
{c7} is non empty set
{{c7,(- C)},{c7}} is non empty set
the addF of V . [c7,(- C)] is set
(c7 - C) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 - C),x) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 - C),x] is set
{(c7 - C),x} is non empty set
{(c7 - C)} is non empty set
{{(c7 - C),x},{(c7 - C)}} is non empty set
the addF of V . [(c7 - C),x] is set
u - C is left_complementable right_complementable complementable Element of the carrier of V
u + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
C + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(- C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(C - C)) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
W + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(0. V)) is left_complementable right_complementable 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
B + (c7 - C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,(c7 - C)) is left_complementable right_complementable complementable Element of the carrier of V
[B,(c7 - C)] is set
{B,(c7 - C)} is non empty set
{{B,(c7 - C)},{B}} is non empty set
the addF of V . [B,(c7 - C)] is set
(B + (c7 - C)) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((B + (c7 - C)),x) is left_complementable right_complementable complementable Element of the carrier of V
[(B + (c7 - C)),x] is set
{(B + (c7 - C)),x} is non empty set
{(B + (c7 - C))} is non empty set
{{(B + (c7 - C)),x},{(B + (c7 - C))}} is non empty set
the addF of V . [(B + (c7 - C)),x] is set
B + ((c7 - C) + x) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,((c7 - C) + x)) is left_complementable right_complementable complementable Element of the carrier of V
[B,((c7 - C) + x)] is set
{B,((c7 - C) + x)} is non empty set
{{B,((c7 - C) + x)},{B}} is non empty set
the addF of V . [B,((c7 - C) + x)] is set
x is set
x is left_complementable right_complementable complementable Element of the carrier of V
B + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,x) is left_complementable right_complementable 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 addF of V . [B,x] is set
C - c7 is left_complementable right_complementable complementable Element of the carrier of V
- c7 is left_complementable right_complementable complementable Element of the carrier of V
C + (- c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(- c7)) is left_complementable right_complementable complementable Element of the carrier of V
[C,(- c7)] is set
{C,(- c7)} is non empty set
{C} is non empty set
{{C,(- c7)},{C}} is non empty set
the addF of V . [C,(- c7)] is set
(C - c7) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((C - c7),x) is left_complementable right_complementable complementable Element of the carrier of V
[(C - c7),x] is set
{(C - c7),x} is non empty set
{(C - c7)} is non empty set
{{(C - c7),x},{(C - c7)}} is non empty set
the addF of V . [(C - c7),x] is set
u - c7 is left_complementable right_complementable complementable Element of the carrier of V
u + (- c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- c7)) is left_complementable right_complementable complementable Element of the carrier of V
[u,(- c7)] is set
{u,(- c7)} is non empty set
{u} is non empty set
{{u,(- c7)},{u}} is non empty set
the addF of V . [u,(- c7)] is set
c7 - c7 is left_complementable right_complementable complementable Element of the carrier of V
c7 + (- c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(- c7)) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(- c7)] is set
{c7,(- c7)} is non empty set
{c7} is non empty set
{{c7,(- c7)},{c7}} is non empty set
the addF of V . [c7,(- c7)] is set
B + (c7 - c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,(c7 - c7)) is left_complementable right_complementable complementable Element of the carrier of V
[B,(c7 - c7)] is set
{B,(c7 - c7)} is non empty set
{{B,(c7 - c7)},{B}} is non empty set
the addF of V . [B,(c7 - c7)] is set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
B + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (B,(0. V)) is left_complementable right_complementable complementable Element of the carrier of V
[B,(0. V)] is set
{B,(0. V)} is non empty set
{{B,(0. V)},{B}} is non empty set
the addF of V . [B,(0. V)] is set
W + (C - c7) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(C - c7)) is left_complementable right_complementable complementable Element of the carrier of V
[W,(C - c7)] is set
{W,(C - c7)} is non empty set
{{W,(C - c7)},{W}} is non empty set
the addF of V . [W,(C - c7)] is set
(W + (C - c7)) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W + (C - c7)),x) is left_complementable right_complementable complementable Element of the carrier of V
[(W + (C - c7)),x] is set
{(W + (C - c7)),x} is non empty set
{(W + (C - c7))} is non empty set
{{(W + (C - c7)),x},{(W + (C - c7))}} is non empty set
the addF of V . [(W + (C - c7)),x] is set
W + ((C - c7) + x) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,((C - c7) + x)) is left_complementable right_complementable complementable Element of the carrier of V
[W,((C - c7) + x)] is set
{W,((C - c7) + x)} is non empty set
{{W,((C - c7) + x)},{W}} is non empty set
the addF of V . [W,((C - c7) + x)] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,(- W),B) is Element of bool the carrier of V
{ ((- W) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is V31() real V33() Element of REAL
W * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,u) is set
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the Mult of V . [W,u] is set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
W - 1 is V31() real V33() Element of REAL
C is left_complementable right_complementable complementable Element of the carrier of V
u + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
C + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(0. V)) is left_complementable right_complementable 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
u - u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(u - u)) is left_complementable right_complementable 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 * u) - u is left_complementable right_complementable complementable Element of the carrier of V
(W * u) + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W * u),(- u)) is left_complementable right_complementable 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
1 * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (1,u) is set
[1,u] is set
{1,u} is non empty set
{1} is non empty set
{{1,u},{1}} is non empty set
the Mult of V . [1,u] is set
(W * u) - (1 * u) is left_complementable right_complementable complementable Element of the carrier of V
- (1 * u) is left_complementable right_complementable complementable Element of the carrier of V
(W * u) + (- (1 * u)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W * u),(- (1 * u))) is left_complementable right_complementable complementable Element of the carrier of V
[(W * u),(- (1 * u))] is set
{(W * u),(- (1 * u))} is non empty set
{{(W * u),(- (1 * u))},{(W * u)}} is non empty set
the addF of V . [(W * u),(- (1 * u))] is set
(W - 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((W - 1),u) is set
[(W - 1),u] is set
{(W - 1),u} is non empty set
{(W - 1)} is non empty set
{{(W - 1),u},{(W - 1)}} is non empty set
the Mult of V . [(W - 1),u] is set
(W - 1) " is V31() real V33() Element of REAL
((W - 1) ") * C is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (((W - 1) "),C) is set
[((W - 1) "),C] is set
{((W - 1) "),C} is non empty set
{((W - 1) ")} is non empty set
{{((W - 1) "),C},{((W - 1) ")}} is non empty set
the Mult of V . [((W - 1) "),C] is set
((W - 1) ") * (W - 1) is V31() real V33() Element of REAL
(((W - 1) ") * (W - 1)) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((((W - 1) ") * (W - 1)),u) is set
[(((W - 1) ") * (W - 1)),u] is set
{(((W - 1) ") * (W - 1)),u} is non empty set
{(((W - 1) ") * (W - 1))} is non empty set
{{(((W - 1) ") * (W - 1)),u},{(((W - 1) ") * (W - 1))}} is non empty set
the Mult of V . [(((W - 1) ") * (W - 1)),u] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is V31() real V33() Element of REAL
W * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (W,u) is set
[W,u] is set
{W,u} is non empty set
{W} is non empty set
{{W,u},{W}} is non empty set
the Mult of V . [W,u] is set
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
W - 1 is V31() real V33() Element of REAL
(W - 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . ((W - 1),u) is set
[(W - 1),u] is set
{(W - 1),u} is non empty set
{(W - 1)} is non empty set
{{(W - 1),u},{(W - 1)}} is non empty set
the Mult of V . [(W - 1),u] is set
(W - 1) + 1 is V31() real V33() Element of REAL
((W - 1) + 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (((W - 1) + 1),u) is set
[((W - 1) + 1),u] is set
{((W - 1) + 1),u} is non empty set
{((W - 1) + 1)} is non empty set
{{((W - 1) + 1),u},{((W - 1) + 1)}} is non empty set
the Mult of V . [((W - 1) + 1),u] is set
1 * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V . (1,u) is set
[1,u] is set
{1,u} is non empty set
{1} is non empty set
{{1,u},{1}} is non empty set
the Mult of V . [1,u] is set
((W - 1) * u) + (1 * u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 - 1) * u),(1 * u)) is left_complementable right_complementable complementable Element of the carrier of V
[((W - 1) * u),(1 * u)] is set
{((W - 1) * u),(1 * u)} is non empty set
{((W - 1) * u)} is non empty set
{{((W - 1) * u),(1 * u)},{((W - 1) * u)}} is non empty set
the addF of V . [((W - 1) * u),(1 * u)] is set
u + ((W - 1) * u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,((W - 1) * u)) is left_complementable right_complementable complementable Element of the carrier of V
[u,((W - 1) * u)] is set
{u,((W - 1) * u)} is non empty set
{u} is non empty set
{{u,((W - 1) * u)},{u}} is non empty set
the addF of V . [u,((W - 1) * u)] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
(- 1) * u is left_complementable right_complementable complementable Element of the carrier of V
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
the Mult of V . ((- 1),u) is set
[(- 1),u] is set
{(- 1),u} is non empty set
{(- 1)} is non empty set
{{(- 1),u},{(- 1)}} is non empty set
the Mult of V . [(- 1),u] is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u + W is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,C) is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u - W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
u + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(- W) + u is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((- W),u) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
C is left_complementable right_complementable complementable Element of the carrier of V
W - C is left_complementable right_complementable complementable Element of the carrier of V
- C is left_complementable right_complementable complementable Element of the carrier of V
W + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(- C)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
W - C is left_complementable right_complementable complementable Element of the carrier of V
- C is left_complementable right_complementable complementable Element of the carrier of V
W + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u - W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
u + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
C is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
C + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,C) is left_complementable right_complementable 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
c7 is left_complementable right_complementable complementable Element of the carrier of V
C + c7 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,c7) is left_complementable right_complementable complementable Element of the carrier of V
[C,c7] is set
{C,c7} is non empty set
{{C,c7},{C}} is non empty set
the addF of V . [C,c7] is set
c7 + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,C) is left_complementable right_complementable complementable Element of the carrier of V
[c7,C] is set
{c7,C} is non empty set
{c7} is non empty set
{{c7,C},{c7}} is non empty set
the addF of V . [c7,C] is set
- C is left_complementable right_complementable complementable Element of the carrier of V
(- C) - C is left_complementable right_complementable complementable Element of the carrier of V
- C is left_complementable right_complementable complementable Element of the carrier of V
(- C) + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((- C),(- C)) is left_complementable right_complementable 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
(c7 + C) + ((- C) - C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + C),((- C) - C)) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + C),((- C) - C)] is set
{(c7 + C),((- C) - C)} is non empty set
{(c7 + C)} is non empty set
{{(c7 + C),((- C) - C)},{(c7 + C)}} is non empty set
the addF of V . [(c7 + C),((- C) - C)] is set
(c7 + C) + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + C),(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + C),(- C)] is set
{(c7 + C),(- C)} is non empty set
{{(c7 + C),(- C)},{(c7 + C)}} is non empty set
the addF of V . [(c7 + C),(- C)] is set
((c7 + C) + (- C)) - C is left_complementable right_complementable complementable Element of the carrier of V
((c7 + C) + (- C)) + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (((c7 + C) + (- C)),(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[((c7 + C) + (- C)),(- C)] is set
{((c7 + C) + (- C)),(- C)} is non empty set
{((c7 + C) + (- C))} is non empty set
{{((c7 + C) + (- C)),(- C)},{((c7 + C) + (- C))}} is non empty set
the addF of V . [((c7 + C) + (- C)),(- C)] is set
C + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(- C)) is left_complementable right_complementable 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
c7 + (C + (- C)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(C + (- C))) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(C + (- C))] is set
{c7,(C + (- C))} is non empty set
{{c7,(C + (- C))},{c7}} is non empty set
the addF of V . [c7,(C + (- C))] is set
(c7 + (C + (- C))) - C is left_complementable right_complementable complementable Element of the carrier of V
(c7 + (C + (- C))) + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + (C + (- C))),(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + (C + (- C))),(- C)] is set
{(c7 + (C + (- C))),(- C)} is non empty set
{(c7 + (C + (- C)))} is non empty set
{{(c7 + (C + (- C))),(- C)},{(c7 + (C + (- C)))}} is non empty set
the addF of V . [(c7 + (C + (- C))),(- C)] is set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
c7 + (0. V) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(0. V)) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(0. V)] is set
{c7,(0. V)} is non empty set
{{c7,(0. V)},{c7}} is non empty set
the addF of V . [c7,(0. V)] is set
(c7 + (0. V)) - C is left_complementable right_complementable complementable Element of the carrier of V
(c7 + (0. V)) + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((c7 + (0. V)),(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[(c7 + (0. V)),(- C)] is set
{(c7 + (0. V)),(- C)} is non empty set
{(c7 + (0. V))} is non empty set
{{(c7 + (0. V)),(- C)},{(c7 + (0. V))}} is non empty set
the addF of V . [(c7 + (0. V)),(- C)] is set
c7 - C is left_complementable right_complementable complementable Element of the carrier of V
c7 + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (c7,(- C)) is left_complementable right_complementable complementable Element of the carrier of V
[c7,(- C)] is set
{c7,(- C)} is non empty set
{{c7,(- C)},{c7}} is non empty set
the addF of V . [c7,(- C)] is set
- (u - W) is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
u + (- (u - W)) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- (u - W))) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(- u) + W is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((- u),W) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,((- u) + W)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u + (- u)),W) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(0. V) + W is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((0. V),W) is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,W,B) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
W + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
W + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,C) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(W + C) - u is left_complementable right_complementable complementable Element of the carrier of V
(W + C) + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W + C),(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(W - u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
W + u is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,u) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
(W + u) + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W + u),(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(u - u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(0. V)) is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,W,B) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
u + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
u + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- W)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u - C is left_complementable right_complementable complementable Element of the carrier of V
- C is left_complementable right_complementable complementable Element of the carrier of V
u + (- C) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- C)) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(u + C) - W is left_complementable right_complementable complementable Element of the carrier of V
(u + C) + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u + C),(- W)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (C,(u - W)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u - u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u - u),W) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((0. V),W) is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
B is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(V,u,B) is Element of bool the carrier of V
{ (u + b1) where b1 is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,x) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + C is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,x) is left_complementable right_complementable 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
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(V,W,C) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
W + u1 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,u1) is left_complementable right_complementable 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 V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(0. V) + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((0. V),x) is left_complementable right_complementable 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 - u is left_complementable right_complementable complementable Element of the carrier of V
- u is left_complementable right_complementable complementable Element of the carrier of V
u + (- u) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,(- u)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u - u),x) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((- u),(W + u1)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,((- u) + (W + u1))) is left_complementable right_complementable 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
(V,(u + ((- u) + (W + u1))),B) is Element of bool the carrier of V
{ ((u + ((- u) + (W + u1))) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(u - u) + (W + u1) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((u - u),(W + u1)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((0. V),(W + u1)) is left_complementable right_complementable 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
(V,(W + u1),C) is Element of bool the carrier of V
{ ((W + u1) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in C } is set
(V,(W + u1),B) is Element of bool the carrier of V
{ ((W + u1) + b1) where b1 is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
W + x is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,x) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
u + u1 is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (u,u1) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((0. V),x) is left_complementable right_complementable 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 - W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
W + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,(- W)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W - W),x) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((- W),(u + u1)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . (W,((- W) + (u + u1))) is left_complementable right_complementable 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
(V,(W + ((- W) + (u + u1))),C) is Element of bool the carrier of V
{ ((W + ((- W) + (u + u1))) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in C } is set
(W - W) + (u + u1) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((W - W),(u + u1)) is left_complementable right_complementable 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 left_complementable right_complementable complementable Element of the carrier of V
the addF of V . ((0. V),(u + u1)) is left_complementable right_complementable 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
(V,(u + u1),B) is Element of bool the carrier of V
{ ((u + u1) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,(u + u1),C) is Element of bool the carrier of V
{ ((u + u1) + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in C } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is (V,u)
the carrier of V is non empty set
B is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in u } is set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
W is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
B is (V,u)
C is (V,W)
the carrier of V is non empty set
C is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in u } is set
c7 is left_complementable right_complementable complementable Element of the carrier of V
(V,c7,W) is Element of bool the carrier of V
{ (c7 + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
u is left_complementable right_complementable 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
(V,u,(V)) is Element of bool the carrier of V
{ (u + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in (V) } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
u is Element of bool the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
(V,W,(V)) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in (V) } is set
{W} is non empty Element of bool the carrier of V
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in u } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict RLSStruct
the left_complementable right_complementable complementable Element of the carrier of V is left_complementable right_complementable 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
(V, the left_complementable right_complementable complementable Element of the carrier of V,(V)) is Element of bool the carrier of V
{ ( the left_complementable right_complementable complementable Element of the carrier of V + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in (V) } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
bool the carrier of V is non empty set
(V) is non empty left_complementable right_complementable complementable strict Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:REAL, the carrier of V:] -defined the carrier of V -valued Function-like V18([:REAL, the carrier of V:], the carrier of V) Element of bool [:[:REAL, the carrier of V:], the carrier of V:]
[:REAL, the carrier of V:] is non empty set
[:[:REAL, the carrier of V:], the carrier of V:] is non empty set
bool [:[:REAL, the carrier of V:], the carrier of V:] is non empty set
RLSStruct(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V #) is non empty strict RLSStruct
u is Element of bool the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
(V,W,(V)) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in (V) } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
0. V is V55(V) left_complementable right_complementable complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is left_complementable right_complementable complementable Element of the carrier of V
u is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
the carrier of u is non empty set
W is (V,u)
B is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in u } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
B is (V,W)
C is left_complementable right_complementable complementable Element of the carrier of V
(V,C,W) is Element of bool the carrier of V
{ (C + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
C is (V,B)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,W,B) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
B is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
C is (V,B)
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
(V,W,B) is Element of bool the carrier of V
{ (W + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is left_complementable right_complementable complementable Element of the carrier of V
u - W is left_complementable right_complementable complementable Element of the carrier of V
- W is left_complementable right_complementable complementable Element of the carrier of V
u + (- W) is left_complementable right_complementable complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued 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 non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is 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 left_complementable right_complementable 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 left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
C is (V,B)
C is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in B } is set
C is (V,B)
V is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() RLSStruct
the carrier of V is non empty set
u is left_complementable right_complementable complementable Element of the carrier of V
W is non empty left_complementable right_complementable complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital V106() (V)
B is (V,W)
C is (V,W)
C is left_complementable right_complementable complementable Element of the carrier of V
(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 left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set
c7 is left_complementable right_complementable complementable Element of the carrier of V
(V,c7,W) is Element of bool the carrier of V
{ (c7 + b1) where b1 is left_complementable right_complementable complementable Element of the carrier of V : b1 in W } is set