:: RUSUB_2 semantic presentation

K93() is V33() V34() V35() V39() set
K97() is V33() V34() V35() V36() V37() V38() V39() Element of bool K93()
bool K93() is non empty set
K92() is V33() V34() V35() V36() V37() V38() V39() set
bool K92() is non empty set
bool K97() is non empty set
[:K97(),K93():] is Relation-like set
bool [:K97(),K93():] is non empty set
{} is set
the Relation-like non-empty empty-yielding empty V33() V34() V35() V36() V37() V38() V39() set is Relation-like non-empty empty-yielding empty V33() V34() V35() V36() V37() V38() V39() set
1 is non empty V30() V31() V32() V33() V34() V35() V36() V37() V38() Element of K97()
0 is V30() V31() V32() V33() V34() V35() V36() V37() V38() Element of K97()

the carrier of V is non empty set

{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
bool the carrier of V is non empty set
the carrier of W1 is non empty set
the carrier of W2 is non empty set
B is set
C is Element of the carrier of V
AC is Element of the carrier of V
C + AC is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
(0. V) + (0. V) is Element of the carrier of V
B is Element of bool the carrier of V
W3 is Element of bool the carrier of V
S is Element of bool the carrier of V
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W3 & b2 in S ) } is set
C is set
AC is Element of the carrier of V
BC is Element of the carrier of V
AC + BC is Element of the carrier of V
C is set
AC is Element of the carrier of V
BC is Element of the carrier of V
AC + BC is Element of the carrier of V

the carrier of W3 is non empty set

the carrier of S is non empty set

the carrier of W1 is non empty set

the carrier of W2 is non empty set
the carrier of W1 /\ the carrier of W2 is set
the carrier of V is non empty set
0. V is V56(V) Element of the carrier of V
the carrier of V /\ the carrier of V is set
bool the carrier of V is non empty set
B is Element of bool the carrier of V
C is Element of bool the carrier of V
AC is Element of bool the carrier of V

the carrier of W3 is non empty set

the carrier of S is non empty set

the carrier of V is non empty set

W3 is set
the carrier of (V,W1,W2) is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
S is Element of the carrier of V
A is Element of the carrier of V
S + A is Element of the carrier of V
S is Element of the carrier of V
A is Element of the carrier of V
S + A is Element of the carrier of V
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
the carrier of (V,W1,W2) is non empty set

the carrier of V is non empty set

W3 is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
W3 + (0. V) is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
(0. V) + W3 is Element of the carrier of V

W3 is set
the carrier of (V,W1,W2) is non empty set
the carrier of W1 is non empty set
the carrier of W2 is non empty set
the carrier of W1 /\ the carrier of W2 is set

the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W2 & b2 in W1 ) } is set
A is set
B is Element of the carrier of V
C is Element of the carrier of V
B + C is Element of the carrier of V
the carrier of (V,W1,W2) is non empty set
A is set
B is Element of the carrier of V
C is Element of the carrier of V
B + C is Element of the carrier of V

the carrier of W1 is non empty set

the carrier of (V,W1,W2) is non empty set
W3 is set
the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
A is Element of the carrier of W1
B is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
B + (0. V) is Element of the carrier of V

the carrier of W1 is non empty set

the carrier of W2 is non empty set

the carrier of (V,W1,W2) is non empty set
W3 is set
the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
S is Element of the carrier of V
A is Element of the carrier of V
S + A is Element of the carrier of V

the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W2 & b2 in W3 ) } is set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in (V,W1,W2) & b2 in W3 ) } is set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in (V,W2,W3) ) } is set
the carrier of (V,W1,(V,W2,W3)) is non empty set
AC is set
BC is Element of the carrier of V
L is Element of the carrier of V
BC + L is Element of the carrier of V
the carrier of (V,W1,W2) is non empty set
B9 is Element of the carrier of V
B is Element of the carrier of V
B9 + B is Element of the carrier of V
B + L is Element of the carrier of V
the carrier of (V,W2,W3) is non empty set
B9 + (B + L) is Element of the carrier of V
AC is set
BC is Element of the carrier of V
L is Element of the carrier of V
BC + L is Element of the carrier of V
the carrier of (V,W2,W3) is non empty set
B9 is Element of the carrier of V
B is Element of the carrier of V
B9 + B is Element of the carrier of V
BC + B9 is Element of the carrier of V
the carrier of (V,W1,W2) is non empty set
(BC + B9) + B is Element of the carrier of V

the carrier of W1 is non empty set
the carrier of (V,W1,W2) is non empty set
the carrier of W2 is non empty set

the carrier of (V,W2,W1) is non empty set

the carrier of W1 is non empty set
the carrier of W2 is non empty set

the carrier of ((0). V) is non empty set
the carrier of W1 is non empty set

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the scalar of V is Relation-like [: the carrier of V, the carrier of V:] -defined K93() -valued Function-like V18([: the carrier of V, the carrier of V:],K93()) Element of bool [:[: the carrier of V, the carrier of V:],K93():]
[:[: the carrier of V, the carrier of V:],K93():] is Relation-like set
bool [:[: the carrier of V, the carrier of V:],K93():] is non empty set
UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty strict UNITSTR

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the scalar of V is Relation-like [: the carrier of V, the carrier of V:] -defined K93() -valued Function-like V18([: the carrier of V, the carrier of V:],K93()) Element of bool [:[: the carrier of V, the carrier of V:],K93():]
[:[: the carrier of V, the carrier of V:],K93():] is Relation-like set
bool [:[: the carrier of V, the carrier of V:],K93():] is non empty set
UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty strict UNITSTR

the carrier of UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty set
the carrier of W1 is non empty set
the carrier of () is non empty set

the carrier of W1 is non empty set
the carrier of W1 /\ the carrier of W1 is set

the carrier of (V,W1,W2) is non empty set
the carrier of W2 is non empty set
the carrier of W1 is non empty set
the carrier of W2 /\ the carrier of W1 is set

the carrier of W1 is non empty set
the carrier of W2 is non empty set
the carrier of W3 is non empty set
the carrier of (V,W1,(V,W2,W3)) is non empty set
the carrier of (V,W2,W3) is non empty set
the carrier of W1 /\ the carrier of (V,W2,W3) is set
the carrier of W2 /\ the carrier of W3 is set
the carrier of W1 /\ ( the carrier of W2 /\ the carrier of W3) is set
the carrier of W1 /\ the carrier of W2 is set
( the carrier of W1 /\ the carrier of W2) /\ the carrier of W3 is set
the carrier of (V,W1,W2) is non empty set
the carrier of (V,W1,W2) /\ the carrier of W3 is set

the carrier of (V,W1,W2) is non empty set
the carrier of W1 is non empty set
the carrier of W2 is non empty set
the carrier of W1 /\ the carrier of W2 is set

the carrier of (V,W1,W2) is non empty set
the carrier of W1 is non empty set

the carrier of (V,W2,W1) is non empty set
the carrier of W2 is non empty set

the carrier of W2 is non empty set
the carrier of W1 is non empty set
the carrier of (V,W2,W1) is non empty set
the carrier of W2 /\ the carrier of W1 is set

0. V is V56(V) Element of the carrier of V
the carrier of V is non empty set
the carrier of W1 is non empty set
{(0. V)} is Element of bool the carrier of V
bool the carrier of V is non empty set
{(0. V)} /\ the carrier of W1 is Element of bool the carrier of V
the carrier of (V,((0). V),W1) is non empty set
the carrier of ((0). V) is non empty set
the carrier of ((0). V) /\ the carrier of W1 is set

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the scalar of V is Relation-like [: the carrier of V, the carrier of V:] -defined K93() -valued Function-like V18([: the carrier of V, the carrier of V:],K93()) Element of bool [:[: the carrier of V, the carrier of V:],K93():]
[:[: the carrier of V, the carrier of V:],K93():] is Relation-like set
bool [:[: the carrier of V, the carrier of V:],K93():] is non empty set
UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty strict UNITSTR
the carrier of (V,(),W1) is non empty set
the carrier of W1 is non empty set
the carrier of V /\ the carrier of W1 is set

the carrier of (V,W1,W2) is non empty set

the carrier of (V,W1,W2) is non empty set
the carrier of W1 is non empty set

the carrier of (V,(V,W1,W2),W2) is non empty set
the carrier of W2 is non empty set
W3 is set
the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in (V,W1,W2) & b2 in W2 ) } is set
S is Element of the carrier of V
A is Element of the carrier of V
S + A is Element of the carrier of V
W3 is set

the carrier of (V,W2,(V,W1,W2)) is non empty set

the carrier of (V,W1,(V,W1,W2)) is non empty set
the carrier of W1 is non empty set
W3 is set
the carrier of (V,W1,W2) is non empty set
the carrier of W1 /\ the carrier of (V,W1,W2) is set
W3 is set
the carrier of V is non empty set
S is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
S + (0. V) is Element of the carrier of V
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
the carrier of (V,W1,W2) is non empty set
the carrier of W1 /\ the carrier of (V,W1,W2) is set

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V
the carrier of (V,(V,W1,W2),(V,W2,W3)) is non empty set

the carrier of (V,W2,(V,W1,W3)) is non empty set
S is set
the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in (V,W1,W2) & b2 in (V,W2,W3) ) } is set
A is Element of the carrier of V
B is Element of the carrier of V
A + B is Element of the carrier of V

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

the carrier of (V,W2,(V,W1,W3)) is non empty set

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V
the carrier of (V,(V,W1,W2),(V,W2,W3)) is non empty set
S is set
the carrier of W2 is non empty set
the carrier of (V,W1,W3) is non empty set
the carrier of W2 /\ the carrier of (V,W1,W3) is set
the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W3 ) } is set
A is Element of the carrier of V
B is Element of the carrier of V
A + B is Element of the carrier of V
B + A is Element of the carrier of V
(B + A) - A is Element of the carrier of V
- A is Element of the carrier of V
K187(V,(B + A),(- A)) is Element of the carrier of V
A - A is Element of the carrier of V
K187(V,A,(- A)) is Element of the carrier of V
B + (A - A) is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
B + (0. V) is Element of the carrier of V

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

the carrier of (V,W2,(V,W1,W3)) is non empty set

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V
the carrier of (V,(V,W1,W2),(V,W2,W3)) is non empty set
S is set
the carrier of V is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W2 & b2 in (V,W1,W3) ) } is set
A is Element of the carrier of V
B is Element of the carrier of V
A + B is Element of the carrier of V
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W2 & b2 in W3 ) } is set
the carrier of (V,W2,W3) is non empty set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
the carrier of (V,W1,W2) is non empty set
the carrier of (V,W1,W2) /\ the carrier of (V,W2,W3) is set

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

the carrier of (V,W2,(V,W1,W3)) is non empty set

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V
the carrier of (V,(V,W1,W2),(V,W2,W3)) is non empty set
the carrier of V is non empty set
bool the carrier of V is non empty set
the carrier of W2 is non empty set
S is Element of bool the carrier of V
the carrier of W1 is non empty set
A is set
the carrier of (V,W1,W2) is non empty set
the carrier of (V,W2,W3) is non empty set
the carrier of (V,W1,W2) /\ the carrier of (V,W2,W3) is set
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W1 & b2 in W2 ) } is set
B is Element of the carrier of V
C is Element of the carrier of V
B + C is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
(B + C) + (0. V) is Element of the carrier of V
{ (b1 + b2) where b1, b2 is Element of the carrier of V : ( b1 in W2 & b2 in (V,W1,W3) ) } is set

(V,(V,W1,W2),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

(V,(V,W1,W3),(V,W3,W2)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

(V,(V,W1,W3),(V,W2,W3)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

(V,(V,W1,W3),(V,W3,W2)) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

(V,(V,(V,W1,W3),W3),W2) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

(V,(V,W1,(V,W3,W3)),W2) is non empty V99() Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital strict RealUnitarySpace-like Subspace of V

the carrier of W1 is non empty set

the carrier of W2 is non empty set
the carrier of W1 \/ the carrier of W2 is set

the carrier of A is non empty set
C is set
the carrier of V is non empty set
AC is Element of the carrier of W2
bool the carrier of V is non empty set
L is Element of bool the carrier of V
B9 is set
B is Element of the carrier of W1
x is Element of bool the carrier of V
v is Element of the carrier of V
BC is Element of the carrier of V
v + BC is Element of the carrier of V
(v + BC) - BC is Element of the carrier of V
- BC is Element of the carrier of V
K187(V,(v + BC),(- BC)) is Element of the carrier of V
BC - BC is Element of the carrier of V
K187(V,BC,(- BC)) is Element of the carrier of V
v + (BC - BC) is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
v + (0. V) is Element of the carrier of V
x is Element of bool the carrier of V
BC + v is Element of the carrier of V
(BC + v) - v is Element of the carrier of V
- v is Element of the carrier of V
K187(V,(BC + v),(- v)) is Element of the carrier of V
v - v is Element of the carrier of V
K187(V,v,(- v)) is Element of the carrier of V
BC + (v - v) is Element of the carrier of V
BC + (0. V) is Element of the carrier of V

the carrier of A is non empty set

the carrier of B is non empty set

the carrier of V is non empty set
bool the carrier of V is non empty set
W1 is set
W3 is set

W2 is set
the carrier of A is non empty set
S is set

the carrier of B is non empty set

W3 is set

the carrier of S is non empty set
A is set
[W3,A] is set
{W3,A} is set
{W3} is set
{{W3,A},{W3}} is set
S is set
[W3,S] is set
{W3,S} is set
{W3} is set
{{W3,S},{W3}} is set
dom W2 is set
rng W2 is set
W3 is set
S is set
W2 . S is set
[S,W3] is set
{S,W3} is set
{S} is set
{{S,W3},{S}} is set

the carrier of A is non empty set

the carrier of S is non empty set
A is set
[A,W3] is set
{A,W3} is set
{A} is set
{{A,W3},{A}} is set
W2 . A is set
W1 is set
W2 is set
W3 is set

(V) is set

(V) is non empty set

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the scalar of V is Relation-like [: the carrier of V, the carrier of V:] -defined K93() -valued Function-like V18([: the carrier of V, the carrier of V:],K93()) Element of bool [:[: the carrier of V, the carrier of V:],K93():]
[:[: the carrier of V, the carrier of V:],K93():] is Relation-like set
bool [:[: the carrier of V, the carrier of V:],K93():] is non empty set
UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty strict UNITSTR

W2 is Element of the carrier of V

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the scalar of V is Relation-like [: the carrier of V, the carrier of V:] -defined K93() -valued Function-like V18([: the carrier of V, the carrier of V:],K93()) Element of bool [:[: the carrier of V, the carrier of V:],K93():]
[:[: the carrier of V, the carrier of V:],K93():] is Relation-like set
bool [:[: the carrier of V, the carrier of V:],K93():] is non empty set
UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty strict UNITSTR

W3 is Element of the carrier of V
W3 is Element of the carrier of V
S is Element of the carrier of V
A is Element of the carrier of V
S + A is Element of the carrier of V

(V) is non empty set
W2 is set

W3 is non empty set
[:W3,W3:] is Relation-like non empty set
bool [:W3,W3:] is non empty set
S is Relation-like W3 -defined W3 -valued Element of bool [:W3,W3:]
A is Element of W3
B is Element of W3
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
C is Element of W3
[B,C] is set
{B,C} is set
{B} is set
{{B,C},{B}} is set

[A,C] is set
{A,C} is set
{{A,C},{A}} is set
A is set
the Element of W3 is Element of W3
AC is Element of W3
C is Element of W3
[AC,C] is Element of [:W3,W3:]
{AC,C} is set
{AC} is set
{{AC,C},{AC}} is set
B is set

the carrier of C is non empty set
AC is set

dom B is set
rng B is set
union (rng B) is set
AC is set
BC is set
L is set
B . L is set

the carrier of B9 is non empty set
the carrier of V is non empty set
the Element of rng B is Element of rng B
BC is set
B . BC is set
bool the carrier of V is non empty set
L is Element of bool the carrier of V

the carrier of B9 is non empty set
B9 is Element of the carrier of V
B is Element of the carrier of V
B9 + B is Element of the carrier of V
v is set
x is set
B . x is set
C is set
u is set
B . u is set

the carrier of W1 is non empty set

the carrier of W2 is non empty set
y1 is Element of W3
y2 is Element of W3
[y1,y2] is Element of [:W3,W3:]
{y1,y2} is set
{y1} is set
{{y1,y2},{y1}} is set

B . y2 is set
y2 is Element of W3
y1 is Element of W3
[y2,y1] is Element of [:W3,W3:]
{y2,y1} is set
{y2} is set
{{y2,y1},{y2}} is set

B . y1 is set
y1 is Element of W3
y2 is Element of W3
[y1,y2] is Element of [:W3,W3:]
{y1,y2} is set
{y1} is set
{{y1,y2},{y1}} is set
[y2,y1] is Element of [:W3,W3:]
{y2,y1} is set
{y2} is set
{{y2,y1},{y2}} is set
B9 is V31() V32() Element of K93()
B is Element of the carrier of V
B9 * B is Element of the carrier of V
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the Mult of V . (B9,B) is set
v is set
x is set
B . x is set

the carrier of C is non empty set

the carrier of B9 is non empty set

B is Element of the carrier of V
v is set
x is set
B . x is set

the carrier of C is non empty set

the carrier of ((0). V) is non empty set
0. V is V56(V) Element of the carrier of V
{(0. V)} is Element of bool the carrier of V
B is Element of W3
x is Element of W3
B . x is set

the carrier of C is non empty set
u is Element of the carrier of V
v is Element of W3
[x,v] is Element of [:W3,W3:]
{x,v} is set
{x} is set
{{x,v},{x}} is set
B is Element of W3
A is Element of W3
A is Element of W3

[A,A] is set
{A,A} is set
{A} is set
{{A,A},{A}} is set
A is Element of W3
B is Element of W3
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set

A is Element of W3

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is Relation-like non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the Mult of V is Relation-like [:K93(), the carrier of V:] -defined the carrier of V -valued Function-like V18([:K93(), the carrier of V:], the carrier of V) Element of bool [:[:K93(), the carrier of V:], the carrier of V:]
[:K93(), the carrier of V:] is Relation-like set
[:[:K93(), the carrier of V:], the carrier of V:] is Relation-like set
bool [:[:K93(), the carrier of V:], the carrier of V:] is non empty set
the scalar of V is Relation-like [: the carrier of V, the carrier of V:] -defined K93() -valued Function-like V18([: the carrier of V, the carrier of V:],K93()) Element of bool [:[: the carrier of V, the carrier of V:],K93():]
[:[: the carrier of V, the carrier of V:],K93():] is Relation-like set
bool [:[: the carrier of V, the carrier of V:],K93():] is non empty set
UNITSTR(# the carrier of V, the ZeroF of V, the U7 of V, the Mult of V, the scalar of V #) is non empty strict UNITSTR

C is Element of the carrier of V
0. V is V56(V) Element of the carrier of V
(0. V) + C is Element of the carrier of V
{ (b1 * C) where b1 is V31() V32() Element of K93() : verum } is set
1 * C is Element of the carrier of V
the Mult of V . (1,C) is set
BC is set
L is V31() V32() Element of K93()
L * C is Element of the carrier of V
the Mult of V . (L,C) is set
bool the carrier of V is non empty set
BC is Element of bool the carrier of V
L is Element of the carrier of V
B9 is Element of the carrier of V
L + B9 is Element of the carrier of V
B is V31() V32() Element of K93()
B * C is Element of the carrier of V
the Mult of V . (B,C) is set
v is V31() V32() Element of K93()
v * C is Element of the carrier of V
the Mult of V . (v,C) is set
B + v is V31() V32() Element of K93()
(B + v) * C is Element of the carrier of V
the Mult of V . ((B + v),C) is set
L is V31() V32() Element of K93()
B9 is Element of the carrier of V
L * B9 is Element of the carrier of V
the Mult of V . (L,B9) is set
B is V31() V32() Element of K93()
B * C is Element of the carrier of V
the Mult of V . (B,C) is set
L * B is V31() V32() Element of K93()
(L * B) * C is Element of the carrier of V
the Mult of V . ((L * B),C) is set

the carrier of L is non empty set

B9 is Element of the carrier of V
B is V31() V32() Element of K93()
B * C is Element of the carrier of V
the Mult of V . (B,C) is set
B " is V31() V32() Element of K93()
(B ") * (B * C) is Element of the carrier of V
the Mult of V . ((B "),(B * C)) is set
(B ") * B is V31() V32() Element of K93()
((B ") * B) * C is Element of the carrier of V
the Mult of V . (((B ") * B),C) is set
the carrier of ((0). V) is non empty set
{(0. V)} is Element of bool the carrier of V

B9 is Element of the carrier of V
B is Element of the carrier of V
v is Element of the carrier of V
B + v is Element of the carrier of V
B9 - v is Element of the carrier of V
- v is Element of the carrier of V
K187(V,B9,(- v)) is Element of the carrier of V

B9 is Element of W3
[A,B9] is Element of [:W3,W3:]
{A,B9} is set
{A} is set
{{A,B9},{A}} is set

the carrier of V is non empty set
the ZeroF of V is Element of the carrier of V
the U7 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 Relation-like non empty