:: BILINEAR semantic presentation

K184() is Element of bool K180()
K180() is set
bool K180() is non empty set
K277() is strict doubleLoopStr
the carrier of K277() is set
K134() is set
bool K134() is non empty set
K177() is L6()
the carrier of K177() is set
bool K184() is non empty set
K181() is set
1 is non empty set
[:1,1:] is non empty set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is non empty set
bool [:[:1,1:],1:] is non empty set
{} is set
the empty set is empty set
K is 1-sorted
K is non empty ZeroStr
the carrier of K is non empty set
V is VectSpStr over K
the carrier of V is set
f is VectSpStr over K
the carrier of f is set
[: the carrier of V, the carrier of f:] is set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[:[: the carrier of V, the carrier of f:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
ww is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
A is Element of the carrier of f
w . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{v} is set
{{v,A},{v}} is set
w . [v,A] is set
x . (v,A) is Element of the carrier of K
x . [v,A] is set
w . (v,A) is Element of the carrier of K
w . [v,A] is set
(x . (v,A)) + (w . (v,A)) is Element of the carrier of K
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A is Element of the carrier of V
ww is Element of the carrier of f
v . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
v . [A,ww] is set
x . (A,ww) is Element of the carrier of K
x . [A,ww] is set
w . (A,ww) is Element of the carrier of K
w . [A,ww] is set
(x . (A,ww)) + (w . (A,ww)) is Element of the carrier of K
B . (A,ww) is Element of the carrier of K
B . [A,ww] is set
K is non empty multMagma
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
w is Element of the carrier of K
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
ww is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
A is Element of the carrier of f
w . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{v} is set
{{v,A},{v}} is set
w . [v,A] is set
x . (v,A) is Element of the carrier of K
x . [v,A] is set
w * (x . (v,A)) is Element of the carrier of K
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A is Element of the carrier of V
ww is Element of the carrier of f
v . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
v . [A,ww] is set
x . (A,ww) is Element of the carrier of K
x . [A,ww] is set
w * (x . (A,ww)) is Element of the carrier of K
B . (A,ww) is Element of the carrier of K
B . [A,ww] is set
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
ww is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of f
ww . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
ww . [w,v] is set
x . (w,v) is Element of the carrier of K
x . [w,v] is set
- (x . (w,v)) is Element of the carrier of K
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is Element of the carrier of V
A is Element of the carrier of f
w . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
w . [B,A] is set
x . (B,A) is Element of the carrier of K
x . [B,A] is set
- (x . (B,A)) is Element of the carrier of K
v . (B,A) is Element of the carrier of K
v . [B,A] is set
K is non empty right_complementable add-associative right_zeroed left-distributive left_unital doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
1. K is Element of the carrier of K
the OneF of K is Element of the carrier of K
- (1. K) is Element of the carrier of K
(K,V,f,x,(- (1. K))) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
B is Element of the carrier of f
w . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
w . [v,B] is set
x . (v,B) is Element of the carrier of K
x . [v,B] is set
- (x . (v,B)) is Element of the carrier of K
(- (1. K)) * (x . (v,B)) is Element of the carrier of K
(K,V,f,x,(- (1. K))) . (v,B) is Element of the carrier of K
(K,V,f,x,(- (1. K))) . [v,B] is set
v is Element of the carrier of V
B is Element of the carrier of f
w . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
w . [v,B] is set
x . (v,B) is Element of the carrier of K
x . [v,B] is set
(- (1. K)) * (x . (v,B)) is Element of the carrier of K
- (x . (v,B)) is Element of the carrier of K
(K,V,f,x) . (v,B) is Element of the carrier of K
(K,V,f,x) . [v,B] is set
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is Element of the carrier of V
A is Element of the carrier of f
v . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
v . [B,A] is set
x . (B,A) is Element of the carrier of K
x . [B,A] is set
w . (B,A) is Element of the carrier of K
w . [B,A] is set
(x . (B,A)) - (w . (B,A)) is Element of the carrier of K
(K,V,f,w) . (B,A) is Element of the carrier of K
(K,V,f,w) . [B,A] is set
(x . (B,A)) + ((K,V,f,w) . (B,A)) is Element of the carrier of K
- (w . (B,A)) is Element of the carrier of K
(x . (B,A)) + (- (w . (B,A))) is Element of the carrier of K
B is Element of the carrier of V
A is Element of the carrier of f
v . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
v . [B,A] is set
x . (B,A) is Element of the carrier of K
x . [B,A] is set
w . (B,A) is Element of the carrier of K
w . [B,A] is set
(x . (B,A)) - (w . (B,A)) is Element of the carrier of K
- (w . (B,A)) is Element of the carrier of K
(x . (B,A)) + (- (w . (B,A))) is Element of the carrier of K
(K,V,f,w) . (B,A) is Element of the carrier of K
(K,V,f,w) . [B,A] is set
(x . (B,A)) + ((K,V,f,w) . (B,A)) is Element of the carrier of K
(K,V,f,x,w) . (B,A) is Element of the carrier of K
(K,V,f,x,w) . [B,A] is set
K is non empty Abelian addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,B) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,B,v) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A is Element of the carrier of V
ww is Element of the carrier of f
(K,V,f,v,B) . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
(K,V,f,v,B) . [A,ww] is set
v . (A,ww) is Element of the carrier of K
v . [A,ww] is set
B . (A,ww) is Element of the carrier of K
B . [A,ww] is set
(v . (A,ww)) + (B . (A,ww)) is Element of the carrier of K
(K,V,f,B,v) . (A,ww) is Element of the carrier of K
(K,V,f,B,v) . [A,ww] is set
K is non empty right_zeroed addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
B is Element of the carrier of f
(K,V,f,x,(K,V,f)) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
(K,V,f,x,(K,V,f)) . [v,B] is set
x . (v,B) is Element of the carrier of K
x . [v,B] is set
(K,V,f) . (v,B) is Element of the carrier of K
(K,V,f) . [v,B] is set
(x . (v,B)) + ((K,V,f) . (v,B)) is Element of the carrier of K
(x . (v,B)) + (0. K) is Element of the carrier of K
K is non empty add-associative addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w,v) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w,v)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is Element of the carrier of V
A is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(K,V,f,(K,V,f,x,w),v) . [B,A] is set
(K,V,f,x,w) . (B,A) is Element of the carrier of K
(K,V,f,x,w) . [B,A] is set
v . (B,A) is Element of the carrier of K
v . [B,A] is set
((K,V,f,x,w) . (B,A)) + (v . (B,A)) is Element of the carrier of K
x . (B,A) is Element of the carrier of K
x . [B,A] is set
w . (B,A) is Element of the carrier of K
w . [B,A] is set
(x . (B,A)) + (w . (B,A)) is Element of the carrier of K
((x . (B,A)) + (w . (B,A))) + (v . (B,A)) is Element of the carrier of K
(w . (B,A)) + (v . (B,A)) is Element of the carrier of K
(x . (B,A)) + ((w . (B,A)) + (v . (B,A))) is Element of the carrier of K
(K,V,f,w,v) . (B,A) is Element of the carrier of K
(K,V,f,w,v) . [B,A] is set
(x . (B,A)) + ((K,V,f,w,v) . (B,A)) is Element of the carrier of K
(K,V,f,x,(K,V,f,w,v)) . (B,A) is Element of the carrier of K
(K,V,f,x,(K,V,f,w,v)) . [B,A] is set
K is non empty right_complementable add-associative right_zeroed addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,x)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of f
(K,V,f,x,x) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,x,x) . [w,v] is set
x . (w,v) is Element of the carrier of K
x . [w,v] is set
(x . (w,v)) - (x . (w,v)) is Element of the carrier of K
(K,V,f) . (w,v) is Element of the carrier of K
(K,V,f) . [w,v] is set
K is non empty right-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of K
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w,v) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,(K,V,f,w,v),x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,(K,V,f,w,x),(K,V,f,v,x)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is Element of the carrier of V
A is Element of the carrier of f
(K,V,f,(K,V,f,w,v),x) . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(K,V,f,(K,V,f,w,v),x) . [B,A] is set
(K,V,f,w,v) . (B,A) is Element of the carrier of K
(K,V,f,w,v) . [B,A] is set
x * ((K,V,f,w,v) . (B,A)) is Element of the carrier of K
w . (B,A) is Element of the carrier of K
w . [B,A] is set
v . (B,A) is Element of the carrier of K
v . [B,A] is set
(w . (B,A)) + (v . (B,A)) is Element of the carrier of K
x * ((w . (B,A)) + (v . (B,A))) is Element of the carrier of K
x * (w . (B,A)) is Element of the carrier of K
x * (v . (B,A)) is Element of the carrier of K
(x * (w . (B,A))) + (x * (v . (B,A))) is Element of the carrier of K
(K,V,f,w,x) . (B,A) is Element of the carrier of K
(K,V,f,w,x) . [B,A] is set
((K,V,f,w,x) . (B,A)) + (x * (v . (B,A))) is Element of the carrier of K
(K,V,f,v,x) . (B,A) is Element of the carrier of K
(K,V,f,v,x) . [B,A] is set
((K,V,f,w,x) . (B,A)) + ((K,V,f,v,x) . (B,A)) is Element of the carrier of K
(K,V,f,(K,V,f,w,x),(K,V,f,v,x)) . (B,A) is Element of the carrier of K
(K,V,f,(K,V,f,w,x),(K,V,f,v,x)) . [B,A] is set
K is non empty left-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of K
w is Element of the carrier of K
x + w is Element of the carrier of K
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,(x + w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,(K,V,f,v,x),(K,V,f,v,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is Element of the carrier of V
A is Element of the carrier of f
(K,V,f,v,(x + w)) . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(K,V,f,v,(x + w)) . [B,A] is set
v . (B,A) is Element of the carrier of K
v . [B,A] is set
(x + w) * (v . (B,A)) is Element of the carrier of K
x * (v . (B,A)) is Element of the carrier of K
w * (v . (B,A)) is Element of the carrier of K
(x * (v . (B,A))) + (w * (v . (B,A))) is Element of the carrier of K
(K,V,f,v,x) . (B,A) is Element of the carrier of K
(K,V,f,v,x) . [B,A] is set
((K,V,f,v,x) . (B,A)) + (w * (v . (B,A))) is Element of the carrier of K
(K,V,f,v,w) . (B,A) is Element of the carrier of K
(K,V,f,v,w) . [B,A] is set
((K,V,f,v,x) . (B,A)) + ((K,V,f,v,w) . (B,A)) is Element of the carrier of K
(K,V,f,(K,V,f,v,x),(K,V,f,v,w)) . (B,A) is Element of the carrier of K
(K,V,f,(K,V,f,v,x),(K,V,f,v,w)) . [B,A] is set
K is non empty associative doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of K
w is Element of the carrier of K
x * w is Element of the carrier of K
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,(x * w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,v,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,(K,V,f,v,w),x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is Element of the carrier of V
A is Element of the carrier of f
(K,V,f,v,(x * w)) . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(K,V,f,v,(x * w)) . [B,A] is set
v . (B,A) is Element of the carrier of K
v . [B,A] is set
(x * w) * (v . (B,A)) is Element of the carrier of K
w * (v . (B,A)) is Element of the carrier of K
x * (w * (v . (B,A))) is Element of the carrier of K
(K,V,f,v,w) . (B,A) is Element of the carrier of K
(K,V,f,v,w) . [B,A] is set
x * ((K,V,f,v,w) . (B,A)) is Element of the carrier of K
(K,V,f,(K,V,f,v,w),x) . (B,A) is Element of the carrier of K
(K,V,f,(K,V,f,v,w),x) . [B,A] is set
K is non empty left_unital doubleLoopStr
the carrier of K is non empty set
1. K is Element of the carrier of K
the OneF of K is Element of the carrier of K
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(1. K)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of f
(K,V,f,x,(1. K)) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,x,(1. K)) . [w,v] is set
x . (w,v) is Element of the carrier of K
x . [w,v] is set
(1. K) * (x . (w,v)) is Element of the carrier of K
K is non empty 1-sorted
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
w is Element of the carrier of V
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K is non empty 1-sorted
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
w is Element of the carrier of f
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K is non empty 1-sorted
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
dom (K,V,f,x,w) is Element of bool the carrier of f
bool the carrier of f is non empty set
rng (K,V,f,x,w) is Element of bool the carrier of K
bool the carrier of K is non empty set
dom x is Relation-like the carrier of V -defined the carrier of f -valued Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is non empty set
rng x is Element of bool the carrier of K
B is Relation-like Function-like set
dom B is set
rng B is set
B is Element of the carrier of f
(K,V,f,x,w) . B is Element of the carrier of K
x . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{w} is set
{{w,B},{w}} is set
x . [w,B] is set
A is Relation-like Function-like set
dom A is set
rng A is set
K is non empty 1-sorted
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
dom (K,V,f,x,w) is Element of bool the carrier of V
bool the carrier of V is non empty set
rng (K,V,f,x,w) is Element of bool the carrier of K
bool the carrier of K is non empty set
dom x is Relation-like the carrier of V -defined the carrier of f -valued Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is non empty set
rng x is Element of bool the carrier of K
B is Relation-like Function-like set
dom B is set
rng B is set
B is Element of the carrier of V
(K,V,f,x,w) . B is Element of the carrier of K
x . (B,w) is Element of the carrier of K
[B,w] is set
{B,w} is set
{B} is set
{{B,w},{B}} is set
x . [B,w] is set
A is Relation-like Function-like set
dom A is set
rng A is set
K is non empty ZeroStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
x is Element of the carrier of V
(K,V,f,(K,V,f),x) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f)) . x is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
v is Element of the carrier of f
(K,V,f,(K,V,f),x) . v is Element of the carrier of K
(K,V,f) . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
(K,V,f) . [x,v] is set
(0Functional f) . v is Element of the carrier of K
K is non empty ZeroStr
the carrier of K is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
x is Element of the carrier of f
(K,V,f,(K,V,f),x) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f)) . x is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
v is Element of the carrier of V
(K,V,f,(K,V,f),x) . v is Element of the carrier of K
(K,V,f) . (v,x) is Element of the carrier of K
[v,x] is set
{v,x} is set
{v} is set
{{v,x},{v}} is set
(K,V,f) . [v,x] is set
(0Functional V) . v is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' w is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' w) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) + (K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
B is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . B is Element of the carrier of K
(K,V,f,x,w) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{B} is set
{{B,v},{B}} is set
(K,V,f,x,w) . [B,v] is set
x . (B,v) is Element of the carrier of K
x . [B,v] is set
w . (B,v) is Element of the carrier of K
w . [B,v] is set
(x . (B,v)) + (w . (B,v)) is Element of the carrier of K
(K,V,f,x,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) + (w . (B,v)) is Element of the carrier of K
(K,V,f,w,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) + ((K,V,f,w,v) . B) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . B is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry w is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry w) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) + (K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
B is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . B is Element of the carrier of K
(K,V,f,x,w) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
(K,V,f,x,w) . [v,B] is set
x . (v,B) is Element of the carrier of K
x . [v,B] is set
w . (v,B) is Element of the carrier of K
w . [v,B] is set
(x . (v,B)) + (w . (v,B)) is Element of the carrier of K
(K,V,f,x,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) + (w . (v,B)) is Element of the carrier of K
(K,V,f,w,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) + ((K,V,f,w,v) . B) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . B is Element of the carrier of K
K is non empty doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of K
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
w * (K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
B is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . B is Element of the carrier of K
(K,V,f,x,w) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{B} is set
{{B,v},{B}} is set
(K,V,f,x,w) . [B,v] is set
x . (B,v) is Element of the carrier of K
x . [B,v] is set
w * (x . (B,v)) is Element of the carrier of K
(K,V,f,x,v) . B is Element of the carrier of K
w * ((K,V,f,x,v) . B) is Element of the carrier of K
(w * (K,V,f,x,v)) . B is Element of the carrier of K
K is non empty doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of K
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
w * (K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
B is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . B is Element of the carrier of K
(K,V,f,x,w) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
(K,V,f,x,w) . [v,B] is set
x . (v,B) is Element of the carrier of K
x . [v,B] is set
w * (x . (v,B)) is Element of the carrier of K
(K,V,f,x,v) . B is Element of the carrier of K
w * ((K,V,f,x,v) . B) is Element of the carrier of K
(w * (K,V,f,x,v)) . B is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
(K,V,f,(K,V,f,x),w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x)) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
- (K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x),w) . v is Element of the carrier of K
(K,V,f,x) . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
(K,V,f,x) . [v,w] is set
x . (v,w) is Element of the carrier of K
x . [v,w] is set
- (x . (v,w)) is Element of the carrier of K
(K,V,f,x,w) . v is Element of the carrier of K
- ((K,V,f,x,w) . v) is Element of the carrier of K
(- (K,V,f,x,w)) . v is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
(K,V,f,(K,V,f,x),w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x)) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
- (K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x),w) . v is Element of the carrier of K
(K,V,f,x) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,x) . [w,v] is set
x . (w,v) is Element of the carrier of K
x . [w,v] is set
- (x . (w,v)) is Element of the carrier of K
(K,V,f,x,w) . v is Element of the carrier of K
- ((K,V,f,x,w) . v) is Element of the carrier of K
(- (K,V,f,x,w)) . v is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' w is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' w) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) - (K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
- (K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
(K,V,f,x,v) + (- (K,V,f,w,v)) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
B is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . B is Element of the carrier of K
(K,V,f,x,w) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{B} is set
{{B,v},{B}} is set
(K,V,f,x,w) . [B,v] is set
x . (B,v) is Element of the carrier of K
x . [B,v] is set
w . (B,v) is Element of the carrier of K
w . [B,v] is set
(x . (B,v)) - (w . (B,v)) is Element of the carrier of K
(K,V,f,x,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) - (w . (B,v)) is Element of the carrier of K
(K,V,f,w,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) - ((K,V,f,w,v) . B) is Element of the carrier of K
- ((K,V,f,w,v) . B) is Element of the carrier of K
((K,V,f,x,v) . B) + (- ((K,V,f,w,v) . B)) is Element of the carrier of K
(- (K,V,f,w,v)) . B is Element of the carrier of K
((K,V,f,x,v) . B) + ((- (K,V,f,w,v)) . B) is Element of the carrier of K
((K,V,f,x,v) - (K,V,f,w,v)) . B is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry w is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry w) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) - (K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
- (K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,v) + (- (K,V,f,w,v)) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
B is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . B is Element of the carrier of K
(K,V,f,x,w) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
(K,V,f,x,w) . [v,B] is set
x . (v,B) is Element of the carrier of K
x . [v,B] is set
w . (v,B) is Element of the carrier of K
w . [v,B] is set
(x . (v,B)) - (w . (v,B)) is Element of the carrier of K
(K,V,f,x,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) - (w . (v,B)) is Element of the carrier of K
(K,V,f,w,v) . B is Element of the carrier of K
((K,V,f,x,v) . B) - ((K,V,f,w,v) . B) is Element of the carrier of K
- ((K,V,f,w,v) . B) is Element of the carrier of K
((K,V,f,x,v) . B) + (- ((K,V,f,w,v) . B)) is Element of the carrier of K
(- (K,V,f,w,v)) . B is Element of the carrier of K
((K,V,f,x,v) . B) + ((- (K,V,f,w,v)) . B) is Element of the carrier of K
((K,V,f,x,v) - (K,V,f,w,v)) . B is Element of the carrier of K
K is non empty multMagma
V is non empty VectSpStr over K
the carrier of V is non empty set
the carrier of K is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
ww is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
A is Element of the carrier of f
w . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{v} is set
{{v,A},{v}} is set
w . [v,A] is set
x . v is Element of the carrier of K
w . A is Element of the carrier of K
(x . v) * (w . A) is Element of the carrier of K
v is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A is Element of the carrier of V
ww is Element of the carrier of f
v . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
v . [A,ww] is set
x . A is Element of the carrier of K
w . ww is Element of the carrier of K
(x . A) * (w . ww) is Element of the carrier of K
B . (A,ww) is Element of the carrier of K
B . [A,ww] is set
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
(K,V,f,x,(0Functional f)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
w is Element of the carrier of V
v is Element of the carrier of f
(K,V,f,x,(0Functional f)) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,x,(0Functional f)) . [w,v] is set
x . w is Element of the carrier of K
(0Functional f) . v is Element of the carrier of K
(x . w) * ((0Functional f) . v) is Element of the carrier of K
(x . w) * (0. K) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed left-distributive doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
x is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,(0Functional V),x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
w is Element of the carrier of V
v is Element of the carrier of f
(K,V,f,(0Functional V),x) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,(0Functional V),x) . [w,v] is set
(0Functional V) . w is Element of the carrier of K
x . v is Element of the carrier of K
((0Functional V) . w) * (x . v) is Element of the carrier of K
(0. K) * (x . v) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
(K,V,f,x,(0Functional f)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of f
(K,V,f,x,(0Functional f)) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,x,(0Functional f)) . [w,v] is set
(K,V,f) . (w,v) is Element of the carrier of K
(K,V,f) . [w,v] is set
K is non empty right_complementable add-associative right_zeroed left-distributive doubleLoopStr
the carrier of K is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of f:] is non empty set
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
x is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,(0Functional V),x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of f
(K,V,f,(0Functional V),x) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,(0Functional V),x) . [w,v] is set
(K,V,f) . (w,v) is Element of the carrier of K
(K,V,f) . [w,v] is set
K is non empty multMagma
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
x . v is Element of the carrier of K
(x . v) * w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
ww is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
(K,V,f,x,w) . (v,ww) is Element of the carrier of K
[v,ww] is set
{v,ww} is set
{v} is set
{{v,ww},{v}} is set
(K,V,f,x,w) . [v,ww] is set
w . ww is Element of the carrier of K
(x . v) * (w . ww) is Element of the carrier of K
((x . v) * w) . ww is Element of the carrier of K
K is non empty commutative multMagma
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
w . v is Element of the carrier of K
(w . v) * x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
ww is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
(K,V,f,x,w) . (ww,v) is Element of the carrier of K
[ww,v] is set
{ww,v} is set
{ww} is set
{{ww,v},{ww}} is set
(K,V,f,x,w) . [ww,v] is set
x . ww is Element of the carrier of K
(x . ww) * (w . v) is Element of the carrier of K
((w . v) * x) . ww is Element of the carrier of K
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
K is non empty multMagma
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
K is non empty right_zeroed addLoopStr
V is non empty VectSpStr over K
f is non empty VectSpStr over K
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
the carrier of V is non empty set
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
x is Element of the carrier of V
(K,V,f,(K,V,f),x) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f)) . x is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
x is Element of the carrier of f
(K,V,f,(K,V,f),x) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f)) . x is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
K is non empty right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
f is non empty VectSpStr over K
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
the carrier of V is non empty set
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
x is Element of the carrier of V
(K,V,f,(K,V,f),x) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f)) . x is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
x is Element of the carrier of f
(K,V,f,(K,V,f),x) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f)) . x is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of f:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
the carrier of K is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) additive Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
ww is Element of the carrier of f
w is Element of the carrier of f
ww + w is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . (ww + w) is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . ww) + ((K,V,f,(K,V,f,x,w),v) . w) is Element of the carrier of K
x . v is Element of the carrier of K
(x . v) * w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) additive Element of bool [: the carrier of f, the carrier of K:]
w . (ww + w) is Element of the carrier of K
(x . v) * (w . (ww + w)) is Element of the carrier of K
w . ww is Element of the carrier of K
w . w is Element of the carrier of K
(w . ww) + (w . w) is Element of the carrier of K
(x . v) * ((w . ww) + (w . w)) is Element of the carrier of K
(x . v) * (w . ww) is Element of the carrier of K
(x . v) * (w . w) is Element of the carrier of K
((x . v) * (w . ww)) + ((x . v) * (w . w)) is Element of the carrier of K
((x . v) * (w . ww)) + ((K,V,f,(K,V,f,x,w),v) . w) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed commutative right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
the carrier of K is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) additive Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
w . v is Element of the carrier of K
(w . v) * x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) additive Element of bool [: the carrier of V, the carrier of K:]
K is non empty right_complementable add-associative right_zeroed associative commutative right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
the carrier of K is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
ww is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
w is Element of the carrier of K
w * ww is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (w,ww) is Element of the carrier of f
[w,ww] is set
{w,ww} is set
{w} is set
{{w,ww},{w}} is set
the lmult of f . [w,ww] is set
(K,V,f,(K,V,f,x,w),v) . (w * ww) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
x . v is Element of the carrier of K
(x . v) * w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
w . (w * ww) is Element of the carrier of K
(x . v) * (w . (w * ww)) is Element of the carrier of K
w . ww is Element of the carrier of K
w * (w . ww) is Element of the carrier of K
(x . v) * (w * (w . ww)) is Element of the carrier of K
(x . v) * (w . ww) is Element of the carrier of K
w * ((x . v) * (w . ww)) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed associative commutative right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
the carrier of K is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
ww is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
w is Element of the carrier of K
w * ww is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (w,ww) is Element of the carrier of V
[w,ww] is set
{w,ww} is set
{w} is set
{{w,ww},{w}} is set
the lmult of V . [w,ww] is set
(K,V,f,(K,V,f,x,w),v) . (w * ww) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
w . v is Element of the carrier of K
(w . v) * x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
x . (w * ww) is Element of the carrier of K
(w . v) * (x . (w * ww)) is Element of the carrier of K
x . ww is Element of the carrier of K
w * (x . ww) is Element of the carrier of K
(w . v) * (w * (x . ww)) is Element of the carrier of K
(w . v) * (x . ww) is Element of the carrier of K
w * ((w . v) * (x . ww)) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
K is non empty non degenerated non trivial doubleLoopStr
V is non empty non trivial VectSpStr over K
the carrier of V is non empty non trivial set
the carrier of K is non empty non trivial set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
the Element of the carrier of f is Element of the carrier of f
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
A is Element of the carrier of V
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
[(0. V),(0. f)] is Element of [: the carrier of V, the carrier of f:]
{(0. V),(0. f)} is set
{(0. V)} is set
{{(0. V),(0. f)},{(0. V)}} is set
[A, the Element of the carrier of f] is Element of [: the carrier of V, the carrier of f:]
{A, the Element of the carrier of f} is set
{A} is set
{{A, the Element of the carrier of f},{A}} is set
dom (K,V,f,x,w) is Relation-like the carrier of V -defined the carrier of f -valued Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is non empty set
(K,V,f,x,w) . ((0. V),(0. f)) is Element of the carrier of K
[(0. V),(0. f)] is set
(K,V,f,x,w) . [(0. V),(0. f)] is set
[[(0. V),(0. f)],((K,V,f,x,w) . ((0. V),(0. f)))] is Element of [:[: the carrier of V, the carrier of f:], the carrier of K:]
{[(0. V),(0. f)],((K,V,f,x,w) . ((0. V),(0. f)))} is set
{[(0. V),(0. f)]} is set
{{[(0. V),(0. f)],((K,V,f,x,w) . ((0. V),(0. f)))},{[(0. V),(0. f)]}} is set
(K,V,f,x,w) . (A, the Element of the carrier of f) is Element of the carrier of K
[A, the Element of the carrier of f] is set
(K,V,f,x,w) . [A, the Element of the carrier of f] is set
[[A, the Element of the carrier of f],((K,V,f,x,w) . (A, the Element of the carrier of f))] is Element of [:[: the carrier of V, the carrier of f:], the carrier of K:]
{[A, the Element of the carrier of f],((K,V,f,x,w) . (A, the Element of the carrier of f))} is set
{[A, the Element of the carrier of f]} is set
{{[A, the Element of the carrier of f],((K,V,f,x,w) . (A, the Element of the carrier of f))},{[A, the Element of the carrier of f]}} is set
ww is set
{ww} is set
ww is set
{ww} is set
K is non empty non degenerated non trivial doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
the carrier of K is non empty non trivial set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty non trivial VectSpStr over K
the carrier of f is non empty non trivial set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
the Element of the carrier of V is Element of the carrier of V
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
A is Element of the carrier of f
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
[(0. V),(0. f)] is Element of [: the carrier of V, the carrier of f:]
{(0. V),(0. f)} is set
{(0. V)} is set
{{(0. V),(0. f)},{(0. V)}} is set
[ the Element of the carrier of V,A] is Element of [: the carrier of V, the carrier of f:]
{ the Element of the carrier of V,A} is set
{ the Element of the carrier of V} is set
{{ the Element of the carrier of V,A},{ the Element of the carrier of V}} is set
dom (K,V,f,x,w) is Relation-like the carrier of V -defined the carrier of f -valued Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is non empty set
(K,V,f,x,w) . ((0. V),(0. f)) is Element of the carrier of K
[(0. V),(0. f)] is set
(K,V,f,x,w) . [(0. V),(0. f)] is set
[[(0. V),(0. f)],((K,V,f,x,w) . ((0. V),(0. f)))] is Element of [:[: the carrier of V, the carrier of f:], the carrier of K:]
{[(0. V),(0. f)],((K,V,f,x,w) . ((0. V),(0. f)))} is set
{[(0. V),(0. f)]} is set
{{[(0. V),(0. f)],((K,V,f,x,w) . ((0. V),(0. f)))},{[(0. V),(0. f)]}} is set
(K,V,f,x,w) . ( the Element of the carrier of V,A) is Element of the carrier of K
[ the Element of the carrier of V,A] is set
(K,V,f,x,w) . [ the Element of the carrier of V,A] is set
[[ the Element of the carrier of V,A],((K,V,f,x,w) . ( the Element of the carrier of V,A))] is Element of [:[: the carrier of V, the carrier of f:], the carrier of K:]
{[ the Element of the carrier of V,A],((K,V,f,x,w) . ( the Element of the carrier of V,A))} is set
{[ the Element of the carrier of V,A]} is set
{{[ the Element of the carrier of V,A],((K,V,f,x,w) . ( the Element of the carrier of V,A))},{[ the Element of the carrier of V,A]}} is set
ww is set
{ww} is set
ww is set
{ww} is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty non trivial set
the carrier of K is non empty non trivial set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty non trivial set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) 0-preserving Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like non constant V20( the carrier of f) V21( the carrier of f, the carrier of K) 0-preserving Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty non trivial Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
B is Element of the carrier of V
x . B is Element of the carrier of K
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
A is Element of the carrier of f
w . A is Element of the carrier of K
(K,V,f,x,w) . (B,A) is Element of the carrier of K
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(K,V,f,x,w) . [B,A] is set
(x . B) * (w . A) is Element of the carrier of K
dom (K,V,f,x,w) is Relation-like the carrier of V -defined the carrier of f -valued Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is non empty set
(K,V,f,x,w) . ((0. V),(0. f)) is Element of the carrier of K
[(0. V),(0. f)] is set
{(0. V),(0. f)} is set
{(0. V)} is set
{{(0. V),(0. f)},{(0. V)}} is set
(K,V,f,x,w) . [(0. V),(0. f)] is set
x . (0. V) is Element of the carrier of K
w . (0. f) is Element of the carrier of K
(x . (0. V)) * (w . (0. f)) is Element of the carrier of K
(0. K) * (w . (0. f)) is Element of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty non trivial set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty non trivial set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty non trivial set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:] is non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
the non empty non trivial Relation-like the carrier of f -defined the carrier of K -valued Function-like non constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:] is non empty non trivial Relation-like the carrier of f -defined the carrier of K -valued Function-like non constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
(K,V,f, the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:], the non empty non trivial Relation-like the carrier of f -defined the carrier of K -valued Function-like non constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]) is non empty non trivial Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like non constant V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty Abelian add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' w is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' w) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
w is Element of the carrier of V
v is Element of the carrier of V
w + v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . (w + v) is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . v is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . w) + ((K,V,f,(K,V,f,x,w),v) . v) is Element of the carrier of K
(K,V,f,x,v) + (K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
((K,V,f,x,v) + (K,V,f,w,v)) . (w + v) is Element of the carrier of K
(K,V,f,x,v) . (w + v) is Element of the carrier of K
(K,V,f,w,v) . (w + v) is Element of the carrier of K
((K,V,f,x,v) . (w + v)) + ((K,V,f,w,v) . (w + v)) is Element of the carrier of K
(K,V,f,x,v) . w is Element of the carrier of K
(K,V,f,x,v) . v is Element of the carrier of K
((K,V,f,x,v) . w) + ((K,V,f,x,v) . v) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . (w + v)) is Element of the carrier of K
(K,V,f,w,v) . w is Element of the carrier of K
(K,V,f,w,v) . v is Element of the carrier of K
((K,V,f,w,v) . w) + ((K,V,f,w,v) . v) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + (((K,V,f,w,v) . w) + ((K,V,f,w,v) . v)) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . w) is Element of the carrier of K
((((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . w)) + ((K,V,f,w,v) . v) is Element of the carrier of K
((K,V,f,x,v) . w) + ((K,V,f,w,v) . w) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,w,v) . w)) + ((K,V,f,x,v) . v) is Element of the carrier of K
((((K,V,f,x,v) . w) + ((K,V,f,w,v) . w)) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . v) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . w is Element of the carrier of K
(((K,V,f,x,v) + (K,V,f,w,v)) . w) + ((K,V,f,x,v) . v) is Element of the carrier of K
((((K,V,f,x,v) + (K,V,f,w,v)) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . v) is Element of the carrier of K
((K,V,f,x,v) . v) + ((K,V,f,w,v) . v) is Element of the carrier of K
(((K,V,f,x,v) + (K,V,f,w,v)) . w) + (((K,V,f,x,v) . v) + ((K,V,f,w,v) . v)) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . v is Element of the carrier of K
(((K,V,f,x,v) + (K,V,f,w,v)) . w) + (((K,V,f,x,v) + (K,V,f,w,v)) . v) is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . w) + (((K,V,f,x,v) + (K,V,f,w,v)) . v) is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . w) + ((K,V,f,(K,V,f,x,w),v) . v) is Element of the carrier of K
K is non empty Abelian add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry w is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry w) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
w is Element of the carrier of f
v is Element of the carrier of f
w + v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . (w + v) is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . v is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . w) + ((K,V,f,(K,V,f,x,w),v) . v) is Element of the carrier of K
(K,V,f,x,v) + (K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
((K,V,f,x,v) + (K,V,f,w,v)) . (w + v) is Element of the carrier of K
(K,V,f,x,v) . (w + v) is Element of the carrier of K
(K,V,f,w,v) . (w + v) is Element of the carrier of K
((K,V,f,x,v) . (w + v)) + ((K,V,f,w,v) . (w + v)) is Element of the carrier of K
(K,V,f,x,v) . w is Element of the carrier of K
(K,V,f,x,v) . v is Element of the carrier of K
((K,V,f,x,v) . w) + ((K,V,f,x,v) . v) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . (w + v)) is Element of the carrier of K
(K,V,f,w,v) . w is Element of the carrier of K
(K,V,f,w,v) . v is Element of the carrier of K
((K,V,f,w,v) . w) + ((K,V,f,w,v) . v) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + (((K,V,f,w,v) . w) + ((K,V,f,w,v) . v)) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . w) is Element of the carrier of K
((((K,V,f,x,v) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . w)) + ((K,V,f,w,v) . v) is Element of the carrier of K
((K,V,f,x,v) . w) + ((K,V,f,w,v) . w) is Element of the carrier of K
(((K,V,f,x,v) . w) + ((K,V,f,w,v) . w)) + ((K,V,f,x,v) . v) is Element of the carrier of K
((((K,V,f,x,v) . w) + ((K,V,f,w,v) . w)) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . v) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . w is Element of the carrier of K
(((K,V,f,x,v) + (K,V,f,w,v)) . w) + ((K,V,f,x,v) . v) is Element of the carrier of K
((((K,V,f,x,v) + (K,V,f,w,v)) . w) + ((K,V,f,x,v) . v)) + ((K,V,f,w,v) . v) is Element of the carrier of K
((K,V,f,x,v) . v) + ((K,V,f,w,v) . v) is Element of the carrier of K
(((K,V,f,x,v) + (K,V,f,w,v)) . w) + (((K,V,f,x,v) . v) + ((K,V,f,w,v) . v)) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . v is Element of the carrier of K
(((K,V,f,x,v) + (K,V,f,w,v)) . w) + (((K,V,f,x,v) + (K,V,f,w,v)) . v) is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . w) + (((K,V,f,x,v) + (K,V,f,w,v)) . v) is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . w) + ((K,V,f,(K,V,f,x,w),v) . v) is Element of the carrier of K
K is non empty right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of K
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
ww is Element of the carrier of V
w is Element of the carrier of V
ww + w is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . (ww + w) is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . ww) + ((K,V,f,(K,V,f,x,w),v) . w) is Element of the carrier of K
w * (K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
(w * (K,V,f,x,v)) . (ww + w) is Element of the carrier of K
(K,V,f,x,v) . (ww + w) is Element of the carrier of K
w * ((K,V,f,x,v) . (ww + w)) is Element of the carrier of K
(K,V,f,x,v) . ww is Element of the carrier of K
(K,V,f,x,v) . w is Element of the carrier of K
((K,V,f,x,v) . ww) + ((K,V,f,x,v) . w) is Element of the carrier of K
w * (((K,V,f,x,v) . ww) + ((K,V,f,x,v) . w)) is Element of the carrier of K
w * ((K,V,f,x,v) . ww) is Element of the carrier of K
w * ((K,V,f,x,v) . w) is Element of the carrier of K
(w * ((K,V,f,x,v) . ww)) + (w * ((K,V,f,x,v) . w)) is Element of the carrier of K
(w * (K,V,f,x,v)) . ww is Element of the carrier of K
((w * (K,V,f,x,v)) . ww) + (w * ((K,V,f,x,v) . w)) is Element of the carrier of K
(w * (K,V,f,x,v)) . w is Element of the carrier of K
((w * (K,V,f,x,v)) . ww) + ((w * (K,V,f,x,v)) . w) is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . ww) + ((w * (K,V,f,x,v)) . w) is Element of the carrier of K
K is non empty right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of K
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
ww is Element of the carrier of f
w is Element of the carrier of f
ww + w is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . (ww + w) is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . ww) + ((K,V,f,(K,V,f,x,w),v) . w) is Element of the carrier of K
w * (K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(w * (K,V,f,x,v)) . (ww + w) is Element of the carrier of K
(K,V,f,x,v) . (ww + w) is Element of the carrier of K
w * ((K,V,f,x,v) . (ww + w)) is Element of the carrier of K
(K,V,f,x,v) . ww is Element of the carrier of K
(K,V,f,x,v) . w is Element of the carrier of K
((K,V,f,x,v) . ww) + ((K,V,f,x,v) . w) is Element of the carrier of K
w * (((K,V,f,x,v) . ww) + ((K,V,f,x,v) . w)) is Element of the carrier of K
w * ((K,V,f,x,v) . ww) is Element of the carrier of K
w * ((K,V,f,x,v) . w) is Element of the carrier of K
(w * ((K,V,f,x,v) . ww)) + (w * ((K,V,f,x,v) . w)) is Element of the carrier of K
(w * (K,V,f,x,v)) . ww is Element of the carrier of K
((w * (K,V,f,x,v)) . ww) + (w * ((K,V,f,x,v) . w)) is Element of the carrier of K
(w * (K,V,f,x,v)) . w is Element of the carrier of K
((w * (K,V,f,x,v)) . ww) + ((w * (K,V,f,x,v)) . w) is Element of the carrier of K
((K,V,f,(K,V,f,x,w),v) . ww) + ((w * (K,V,f,x,v)) . w) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
(K,V,f,(K,V,f,x),w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x)) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
A is Element of the carrier of V
ww is Element of the carrier of V
A + ww is Element of the carrier of V
(K,V,f,(K,V,f,x),w) . (A + ww) is Element of the carrier of K
(K,V,f,(K,V,f,x),w) . A is Element of the carrier of K
(K,V,f,(K,V,f,x),w) . ww is Element of the carrier of K
((K,V,f,(K,V,f,x),w) . A) + ((K,V,f,(K,V,f,x),w) . ww) is Element of the carrier of K
- (K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
(- (K,V,f,x,w)) . (A + ww) is Element of the carrier of K
(K,V,f,x,w) . (A + ww) is Element of the carrier of K
- ((K,V,f,x,w) . (A + ww)) is Element of the carrier of K
(K,V,f,x,w) . A is Element of the carrier of K
(K,V,f,x,w) . ww is Element of the carrier of K
((K,V,f,x,w) . A) + ((K,V,f,x,w) . ww) is Element of the carrier of K
- (((K,V,f,x,w) . A) + ((K,V,f,x,w) . ww)) is Element of the carrier of K
- ((K,V,f,x,w) . A) is Element of the carrier of K
(- ((K,V,f,x,w) . A)) - ((K,V,f,x,w) . ww) is Element of the carrier of K
(- (K,V,f,x,w)) . A is Element of the carrier of K
((- (K,V,f,x,w)) . A) - ((K,V,f,x,w) . ww) is Element of the carrier of K
- ((K,V,f,x,w) . ww) is Element of the carrier of K
((- (K,V,f,x,w)) . A) + (- ((K,V,f,x,w) . ww)) is Element of the carrier of K
(- (K,V,f,x,w)) . ww is Element of the carrier of K
((- (K,V,f,x,w)) . A) + ((- (K,V,f,x,w)) . ww) is Element of the carrier of K
((K,V,f,(K,V,f,x),w) . A) + ((- (K,V,f,x,w)) . ww) is Element of the carrier of K
((K,V,f,(K,V,f,x),w) . A) + ((K,V,f,(K,V,f,x),w) . ww) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
(K,V,f,(K,V,f,x),w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x)) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
A is Element of the carrier of f
ww is Element of the carrier of f
A + ww is Element of the carrier of f
(K,V,f,(K,V,f,x),w) . (A + ww) is Element of the carrier of K
(K,V,f,(K,V,f,x),w) . A is Element of the carrier of K
(K,V,f,(K,V,f,x),w) . ww is Element of the carrier of K
((K,V,f,(K,V,f,x),w) . A) + ((K,V,f,(K,V,f,x),w) . ww) is Element of the carrier of K
- (K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(- (K,V,f,x,w)) . (A + ww) is Element of the carrier of K
(K,V,f,x,w) . (A + ww) is Element of the carrier of K
- ((K,V,f,x,w) . (A + ww)) is Element of the carrier of K
(K,V,f,x,w) . A is Element of the carrier of K
(K,V,f,x,w) . ww is Element of the carrier of K
((K,V,f,x,w) . A) + ((K,V,f,x,w) . ww) is Element of the carrier of K
- (((K,V,f,x,w) . A) + ((K,V,f,x,w) . ww)) is Element of the carrier of K
- ((K,V,f,x,w) . A) is Element of the carrier of K
(- ((K,V,f,x,w) . A)) - ((K,V,f,x,w) . ww) is Element of the carrier of K
(- (K,V,f,x,w)) . A is Element of the carrier of K
((- (K,V,f,x,w)) . A) - ((K,V,f,x,w) . ww) is Element of the carrier of K
- ((K,V,f,x,w) . ww) is Element of the carrier of K
((- (K,V,f,x,w)) . A) + (- ((K,V,f,x,w) . ww)) is Element of the carrier of K
(- (K,V,f,x,w)) . ww is Element of the carrier of K
((- (K,V,f,x,w)) . A) + ((- (K,V,f,x,w)) . ww) is Element of the carrier of K
((K,V,f,(K,V,f,x),w) . A) + ((- (K,V,f,x,w)) . ww) is Element of the carrier of K
((K,V,f,(K,V,f,x),w) . A) + ((K,V,f,(K,V,f,x),w) . ww) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty right_complementable Abelian add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
curry' w is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' w) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
w is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
v is Element of the carrier of K
v * w is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (v,w) is Element of the carrier of V
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
the lmult of V . [v,w] is set
(K,V,f,(K,V,f,x,w),v) . (v * w) is Element of the carrier of K
v * ((K,V,f,(K,V,f,x,w),v) . w) is Element of the carrier of K
(K,V,f,x,v) + (K,V,f,w,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
((K,V,f,x,v) + (K,V,f,w,v)) . (v * w) is Element of the carrier of K
(K,V,f,x,v) . (v * w) is Element of the carrier of K
(K,V,f,w,v) . (v * w) is Element of the carrier of K
((K,V,f,x,v) . (v * w)) + ((K,V,f,w,v) . (v * w)) is Element of the carrier of K
(K,V,f,x,v) . w is Element of the carrier of K
v * ((K,V,f,x,v) . w) is Element of the carrier of K
(v * ((K,V,f,x,v) . w)) + ((K,V,f,w,v) . (v * w)) is Element of the carrier of K
(K,V,f,w,v) . w is Element of the carrier of K
v * ((K,V,f,w,v) . w) is Element of the carrier of K
(v * ((K,V,f,x,v) . w)) + (v * ((K,V,f,w,v) . w)) is Element of the carrier of K
((K,V,f,x,v) . w) + ((K,V,f,w,v) . w) is Element of the carrier of K
v * (((K,V,f,x,v) . w) + ((K,V,f,w,v) . w)) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . w is Element of the carrier of K
v * (((K,V,f,x,v) + (K,V,f,w,v)) . w) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
curry w is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry w) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
w is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . w is Element of the carrier of K
v is Element of the carrier of K
v * w is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (v,w) is Element of the carrier of f
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
the lmult of f . [v,w] is set
(K,V,f,(K,V,f,x,w),v) . (v * w) is Element of the carrier of K
v * ((K,V,f,(K,V,f,x,w),v) . w) is Element of the carrier of K
(K,V,f,x,v) + (K,V,f,w,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
((K,V,f,x,v) + (K,V,f,w,v)) . (v * w) is Element of the carrier of K
(K,V,f,x,v) . (v * w) is Element of the carrier of K
(K,V,f,w,v) . (v * w) is Element of the carrier of K
((K,V,f,x,v) . (v * w)) + ((K,V,f,w,v) . (v * w)) is Element of the carrier of K
(K,V,f,x,v) . w is Element of the carrier of K
v * ((K,V,f,x,v) . w) is Element of the carrier of K
(v * ((K,V,f,x,v) . w)) + ((K,V,f,w,v) . (v * w)) is Element of the carrier of K
(K,V,f,w,v) . w is Element of the carrier of K
v * ((K,V,f,w,v) . w) is Element of the carrier of K
(v * ((K,V,f,x,v) . w)) + (v * ((K,V,f,w,v) . w)) is Element of the carrier of K
((K,V,f,x,v) . w) + ((K,V,f,w,v) . w) is Element of the carrier of K
v * (((K,V,f,x,v) . w) + ((K,V,f,w,v) . w)) is Element of the carrier of K
((K,V,f,x,v) + (K,V,f,w,v)) . w is Element of the carrier of K
v * (((K,V,f,x,v) + (K,V,f,w,v)) . w) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed associative commutative right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of K
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x,w) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x,w)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
ww is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
w is Element of the carrier of K
w * ww is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (w,ww) is Element of the carrier of V
[w,ww] is set
{w,ww} is set
{w} is set
{{w,ww},{w}} is set
the lmult of V . [w,ww] is set
(K,V,f,(K,V,f,x,w),v) . (w * ww) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
w * (K,V,f,x,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
(w * (K,V,f,x,v)) . (w * ww) is Element of the carrier of K
(K,V,f,x,v) . (w * ww) is Element of the carrier of K
w * ((K,V,f,x,v) . (w * ww)) is Element of the carrier of K
(K,V,f,x,v) . ww is Element of the carrier of K
w * ((K,V,f,x,v) . ww) is Element of the carrier of K
w * (w * ((K,V,f,x,v) . ww)) is Element of the carrier of K
w * ((K,V,f,x,v) . ww) is Element of the carrier of K
w * (w * ((K,V,f,x,v) . ww)) is Element of the carrier of K
(w * (K,V,f,x,v)) . ww is Element of the carrier of K
w * ((w * (K,V,f,x,v)) . ww) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed associative commutative right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of K
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
v is Element of the carrier of V
(K,V,f,(K,V,f,x,w),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x,w) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x,w)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
ww is Element of the carrier of f
(K,V,f,(K,V,f,x,w),v) . ww is Element of the carrier of K
w is Element of the carrier of K
w * ww is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (w,ww) is Element of the carrier of f
[w,ww] is set
{w,ww} is set
{w} is set
{{w,ww},{w}} is set
the lmult of f . [w,ww] is set
(K,V,f,(K,V,f,x,w),v) . (w * ww) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
w * (K,V,f,x,v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
(w * (K,V,f,x,v)) . (w * ww) is Element of the carrier of K
(K,V,f,x,v) . (w * ww) is Element of the carrier of K
w * ((K,V,f,x,v) . (w * ww)) is Element of the carrier of K
(K,V,f,x,v) . ww is Element of the carrier of K
w * ((K,V,f,x,v) . ww) is Element of the carrier of K
w * (w * ((K,V,f,x,v) . ww)) is Element of the carrier of K
w * ((K,V,f,x,v) . ww) is Element of the carrier of K
w * (w * ((K,V,f,x,v) . ww)) is Element of the carrier of K
(w * (K,V,f,x,v)) . ww is Element of the carrier of K
w * ((w * (K,V,f,x,v)) . ww) is Element of the carrier of K
w * ((K,V,f,(K,V,f,x,w),v) . ww) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
(K,V,f,(K,V,f,x),w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x) is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x)) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous Element of bool [: the carrier of V, the carrier of K:]
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
A is Element of the carrier of V
(K,V,f,(K,V,f,x),w) . A is Element of the carrier of K
ww is Element of the carrier of K
ww * A is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (ww,A) is Element of the carrier of V
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
the lmult of V . [ww,A] is set
(K,V,f,(K,V,f,x),w) . (ww * A) is Element of the carrier of K
ww * ((K,V,f,(K,V,f,x),w) . A) is Element of the carrier of K
- (K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
(- (K,V,f,x,w)) . (ww * A) is Element of the carrier of K
(K,V,f,x,w) . (ww * A) is Element of the carrier of K
- ((K,V,f,x,w) . (ww * A)) is Element of the carrier of K
(K,V,f,x,w) . A is Element of the carrier of K
ww * ((K,V,f,x,w) . A) is Element of the carrier of K
- (ww * ((K,V,f,x,w) . A)) is Element of the carrier of K
- ((K,V,f,x,w) . A) is Element of the carrier of K
ww * (- ((K,V,f,x,w) . A)) is Element of the carrier of K
(- (K,V,f,x,w)) . A is Element of the carrier of K
ww * ((- (K,V,f,x,w)) . A) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
(K,V,f,(K,V,f,x),w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x) is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x)) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous Element of bool [: the carrier of f, the carrier of K:]
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
A is Element of the carrier of f
(K,V,f,(K,V,f,x),w) . A is Element of the carrier of K
ww is Element of the carrier of K
ww * A is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (ww,A) is Element of the carrier of f
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
the lmult of f . [ww,A] is set
(K,V,f,(K,V,f,x),w) . (ww * A) is Element of the carrier of K
ww * ((K,V,f,(K,V,f,x),w) . A) is Element of the carrier of K
- (K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(- (K,V,f,x,w)) . (ww * A) is Element of the carrier of K
(K,V,f,x,w) . (ww * A) is Element of the carrier of K
- ((K,V,f,x,w) . (ww * A)) is Element of the carrier of K
(K,V,f,x,w) . A is Element of the carrier of K
ww * ((K,V,f,x,w) . A) is Element of the carrier of K
- (ww * ((K,V,f,x,w) . A)) is Element of the carrier of K
- ((K,V,f,x,w) . A) is Element of the carrier of K
ww * (- ((K,V,f,x,w) . A)) is Element of the carrier of K
(- (K,V,f,x,w)) . A is Element of the carrier of K
ww * ((- (K,V,f,x,w)) . A) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x,(K,V,f,w)) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of V
x + w is Element of the carrier of V
v is Element of the carrier of f
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B . ((x + w),v) is Element of the carrier of K
[(x + w),v] is set
{(x + w),v} is set
{(x + w)} is set
{{(x + w),v},{(x + w)}} is set
B . [(x + w),v] is set
B . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
B . [x,v] is set
B . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
B . [w,v] is set
(B . (x,v)) + (B . (w,v)) is Element of the carrier of K
(K,V,f,B,v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' B is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' B) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,B,v) . (x + w) is Element of the carrier of K
(K,V,f,B,v) . x is Element of the carrier of K
(K,V,f,B,v) . w is Element of the carrier of K
((K,V,f,B,v) . x) + ((K,V,f,B,v) . w) is Element of the carrier of K
(B . (x,v)) + ((K,V,f,B,v) . w) is Element of the carrier of K
K is non empty addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of f
v is Element of the carrier of f
w + v is Element of the carrier of f
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B . (x,(w + v)) is Element of the carrier of K
[x,(w + v)] is set
{x,(w + v)} is set
{x} is set
{{x,(w + v)},{x}} is set
B . [x,(w + v)] is set
B . (x,w) is Element of the carrier of K
[x,w] is set
{x,w} is set
{{x,w},{x}} is set
B . [x,w] is set
B . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{{x,v},{x}} is set
B . [x,v] is set
(B . (x,w)) + (B . (x,v)) is Element of the carrier of K
(K,V,f,B,x) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry B is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry B) . x is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,B,x) . (w + v) is Element of the carrier of K
(K,V,f,B,x) . w is Element of the carrier of K
(K,V,f,B,x) . v is Element of the carrier of K
((K,V,f,B,x) . w) + ((K,V,f,B,x) . v) is Element of the carrier of K
(B . (x,w)) + ((K,V,f,B,x) . v) is Element of the carrier of K
K is non empty right_zeroed addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of V
x + w is Element of the carrier of V
v is Element of the carrier of f
B is Element of the carrier of f
v + B is Element of the carrier of f
A is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A . ((x + w),(v + B)) is Element of the carrier of K
[(x + w),(v + B)] is set
{(x + w),(v + B)} is set
{(x + w)} is set
{{(x + w),(v + B)},{(x + w)}} is set
A . [(x + w),(v + B)] is set
A . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
A . [x,v] is set
A . (x,B) is Element of the carrier of K
[x,B] is set
{x,B} is set
{{x,B},{x}} is set
A . [x,B] is set
(A . (x,v)) + (A . (x,B)) is Element of the carrier of K
A . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
A . [w,v] is set
A . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{{w,B},{w}} is set
A . [w,B] is set
(A . (w,v)) + (A . (w,B)) is Element of the carrier of K
((A . (x,v)) + (A . (x,B))) + ((A . (w,v)) + (A . (w,B))) is Element of the carrier of K
A . (x,(v + B)) is Element of the carrier of K
[x,(v + B)] is set
{x,(v + B)} is set
{{x,(v + B)},{x}} is set
A . [x,(v + B)] is set
A . (w,(v + B)) is Element of the carrier of K
[w,(v + B)] is set
{w,(v + B)} is set
{{w,(v + B)},{w}} is set
A . [w,(v + B)] is set
(A . (x,(v + B))) + (A . (w,(v + B))) is Element of the carrier of K
((A . (x,v)) + (A . (x,B))) + (A . (w,(v + B))) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
f is non empty right_zeroed VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
x . (w,(0. f)) is Element of the carrier of K
[w,(0. f)] is set
{w,(0. f)} is set
{w} is set
{{w,(0. f)},{w}} is set
x . [w,(0. f)] is set
(0. f) + (0. f) is Element of the carrier of f
x . (w,((0. f) + (0. f))) is Element of the carrier of K
[w,((0. f) + (0. f))] is set
{w,((0. f) + (0. f))} is set
{{w,((0. f) + (0. f))},{w}} is set
x . [w,((0. f) + (0. f))] is set
(x . (w,(0. f))) + (x . (w,(0. f))) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
f is non empty right_zeroed VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
x . ((0. V),w) is Element of the carrier of K
[(0. V),w] is set
{(0. V),w} is set
{(0. V)} is set
{{(0. V),w},{(0. V)}} is set
x . [(0. V),w] is set
(0. V) + (0. V) is Element of the carrier of V
x . (((0. V) + (0. V)),w) is Element of the carrier of K
[((0. V) + (0. V)),w] is set
{((0. V) + (0. V)),w} is set
{((0. V) + (0. V))} is set
{{((0. V) + (0. V)),w},{((0. V) + (0. V))}} is set
x . [((0. V) + (0. V)),w] is set
(x . ((0. V),w)) + (x . ((0. V),w)) is Element of the carrier of K
K is non empty multMagma
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of f
v is Element of the carrier of K
v * x is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (v,x) is Element of the carrier of V
[v,x] is set
{v,x} is set
{v} is set
{{v,x},{v}} is set
the lmult of V . [v,x] is set
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B . ((v * x),w) is Element of the carrier of K
[(v * x),w] is set
{(v * x),w} is set
{(v * x)} is set
{{(v * x),w},{(v * x)}} is set
B . [(v * x),w] is set
B . (x,w) is Element of the carrier of K
[x,w] is set
{x,w} is set
{x} is set
{{x,w},{x}} is set
B . [x,w] is set
v * (B . (x,w)) is Element of the carrier of K
(K,V,f,B,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' B is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' B) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,B,w) . (v * x) is Element of the carrier of K
(K,V,f,B,w) . x is Element of the carrier of K
v * ((K,V,f,B,w) . x) is Element of the carrier of K
K is non empty multMagma
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of f
v is Element of the carrier of K
v * w is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (v,w) is Element of the carrier of f
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
the lmult of f . [v,w] is set
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B . (x,(v * w)) is Element of the carrier of K
[x,(v * w)] is set
{x,(v * w)} is set
{x} is set
{{x,(v * w)},{x}} is set
B . [x,(v * w)] is set
B . (x,w) is Element of the carrier of K
[x,w] is set
{x,w} is set
{{x,w},{x}} is set
B . [x,w] is set
v * (B . (x,w)) is Element of the carrier of K
(K,V,f,B,x) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry B is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry B) . x is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,B,x) . (v * w) is Element of the carrier of K
(K,V,f,B,x) . w is Element of the carrier of K
v * ((K,V,f,B,x) . w) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed associative right-distributive left-distributive distributive left_unital doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of f
x . ((0. V),w) is Element of the carrier of K
[(0. V),w] is set
{(0. V),w} is set
{(0. V)} is set
{{(0. V),w},{(0. V)}} is set
x . [(0. V),w] is set
(0. K) * (0. V) is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((0. K),(0. V)) is Element of the carrier of V
[(0. K),(0. V)] is set
{(0. K),(0. V)} is set
{(0. K)} is set
{{(0. K),(0. V)},{(0. K)}} is set
the lmult of V . [(0. K),(0. V)] is set
x . (((0. K) * (0. V)),w) is Element of the carrier of K
[((0. K) * (0. V)),w] is set
{((0. K) * (0. V)),w} is set
{((0. K) * (0. V))} is set
{{((0. K) * (0. V)),w},{((0. K) * (0. V))}} is set
x . [((0. K) * (0. V)),w] is set
(0. K) * (x . ((0. V),w)) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed associative right-distributive left-distributive distributive left_unital doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w is Element of the carrier of V
x . (w,(0. f)) is Element of the carrier of K
[w,(0. f)] is set
{w,(0. f)} is set
{w} is set
{{w,(0. f)},{w}} is set
x . [w,(0. f)] is set
(0. K) * (0. f) is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . ((0. K),(0. f)) is Element of the carrier of f
[(0. K),(0. f)] is set
{(0. K),(0. f)} is set
{(0. K)} is set
{{(0. K),(0. f)},{(0. K)}} is set
the lmult of f . [(0. K),(0. f)] is set
x . (w,((0. K) * (0. f))) is Element of the carrier of K
[w,((0. K) * (0. f))] is set
{w,((0. K) * (0. f))} is set
{{w,((0. K) * (0. f))},{w}} is set
x . [w,((0. K) * (0. f))] is set
(0. K) * (x . (w,(0. f))) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of V
x - w is Element of the carrier of V
v is Element of the carrier of f
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B . ((x - w),v) is Element of the carrier of K
[(x - w),v] is set
{(x - w),v} is set
{(x - w)} is set
{{(x - w),v},{(x - w)}} is set
B . [(x - w),v] is set
B . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
B . [x,v] is set
B . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
B . [w,v] is set
(B . (x,v)) - (B . (w,v)) is Element of the carrier of K
- w is Element of the carrier of V
x + (- w) is Element of the carrier of V
B . ((x + (- w)),v) is Element of the carrier of K
[(x + (- w)),v] is set
{(x + (- w)),v} is set
{(x + (- w))} is set
{{(x + (- w)),v},{(x + (- w))}} is set
B . [(x + (- w)),v] is set
B . ((- w),v) is Element of the carrier of K
[(- w),v] is set
{(- w),v} is set
{(- w)} is set
{{(- w),v},{(- w)}} is set
B . [(- w),v] is set
(B . (x,v)) + (B . ((- w),v)) is Element of the carrier of K
1. K is Element of the carrier of K
the OneF of K is Element of the carrier of K
- (1. K) is Element of the carrier of K
(- (1. K)) * w is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . ((- (1. K)),w) is Element of the carrier of V
[(- (1. K)),w] is set
{(- (1. K)),w} is set
{(- (1. K))} is set
{{(- (1. K)),w},{(- (1. K))}} is set
the lmult of V . [(- (1. K)),w] is set
B . (((- (1. K)) * w),v) is Element of the carrier of K
[((- (1. K)) * w),v] is set
{((- (1. K)) * w),v} is set
{((- (1. K)) * w)} is set
{{((- (1. K)) * w),v},{((- (1. K)) * w)}} is set
B . [((- (1. K)) * w),v] is set
(B . (x,v)) + (B . (((- (1. K)) * w),v)) is Element of the carrier of K
(- (1. K)) * (B . (w,v)) is Element of the carrier of K
(B . (x,v)) + ((- (1. K)) * (B . (w,v))) is Element of the carrier of K
(1. K) * (B . (w,v)) is Element of the carrier of K
- ((1. K) * (B . (w,v))) is Element of the carrier of K
(B . (x,v)) + (- ((1. K) * (B . (w,v)))) is Element of the carrier of K
(B . (x,v)) - ((1. K) * (B . (w,v))) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of f
v is Element of the carrier of f
w - v is Element of the carrier of f
B is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
B . (x,(w - v)) is Element of the carrier of K
[x,(w - v)] is set
{x,(w - v)} is set
{x} is set
{{x,(w - v)},{x}} is set
B . [x,(w - v)] is set
B . (x,w) is Element of the carrier of K
[x,w] is set
{x,w} is set
{{x,w},{x}} is set
B . [x,w] is set
B . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{{x,v},{x}} is set
B . [x,v] is set
(B . (x,w)) - (B . (x,v)) is Element of the carrier of K
- v is Element of the carrier of f
w + (- v) is Element of the carrier of f
B . (x,(w + (- v))) is Element of the carrier of K
[x,(w + (- v))] is set
{x,(w + (- v))} is set
{{x,(w + (- v))},{x}} is set
B . [x,(w + (- v))] is set
B . (x,(- v)) is Element of the carrier of K
[x,(- v)] is set
{x,(- v)} is set
{{x,(- v)},{x}} is set
B . [x,(- v)] is set
(B . (x,w)) + (B . (x,(- v))) is Element of the carrier of K
1. K is Element of the carrier of K
the OneF of K is Element of the carrier of K
- (1. K) is Element of the carrier of K
(- (1. K)) * v is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . ((- (1. K)),v) is Element of the carrier of f
[(- (1. K)),v] is set
{(- (1. K)),v} is set
{(- (1. K))} is set
{{(- (1. K)),v},{(- (1. K))}} is set
the lmult of f . [(- (1. K)),v] is set
B . (x,((- (1. K)) * v)) is Element of the carrier of K
[x,((- (1. K)) * v)] is set
{x,((- (1. K)) * v)} is set
{{x,((- (1. K)) * v)},{x}} is set
B . [x,((- (1. K)) * v)] is set
(B . (x,w)) + (B . (x,((- (1. K)) * v))) is Element of the carrier of K
(- (1. K)) * (B . (x,v)) is Element of the carrier of K
(B . (x,w)) + ((- (1. K)) * (B . (x,v))) is Element of the carrier of K
(1. K) * (B . (x,v)) is Element of the carrier of K
- ((1. K) * (B . (x,v))) is Element of the carrier of K
(B . (x,w)) + (- ((1. K) * (B . (x,v)))) is Element of the carrier of K
(B . (x,w)) - ((1. K) * (B . (x,v))) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of V
x - w is Element of the carrier of V
v is Element of the carrier of f
B is Element of the carrier of f
v - B is Element of the carrier of f
A is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
A . ((x - w),(v - B)) is Element of the carrier of K
[(x - w),(v - B)] is set
{(x - w),(v - B)} is set
{(x - w)} is set
{{(x - w),(v - B)},{(x - w)}} is set
A . [(x - w),(v - B)] is set
A . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
A . [x,v] is set
A . (x,B) is Element of the carrier of K
[x,B] is set
{x,B} is set
{{x,B},{x}} is set
A . [x,B] is set
(A . (x,v)) - (A . (x,B)) is Element of the carrier of K
A . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
A . [w,v] is set
A . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{{w,B},{w}} is set
A . [w,B] is set
(A . (w,v)) - (A . (w,B)) is Element of the carrier of K
((A . (x,v)) - (A . (x,B))) - ((A . (w,v)) - (A . (w,B))) is Element of the carrier of K
A . (x,(v - B)) is Element of the carrier of K
[x,(v - B)] is set
{x,(v - B)} is set
{{x,(v - B)},{x}} is set
A . [x,(v - B)] is set
A . (w,(v - B)) is Element of the carrier of K
[w,(v - B)] is set
{w,(v - B)} is set
{{w,(v - B)},{w}} is set
A . [w,(v - B)] is set
(A . (x,(v - B))) - (A . (w,(v - B))) is Element of the carrier of K
((A . (x,v)) - (A . (x,B))) - (A . (w,(v - B))) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of V
v is Element of the carrier of f
B is Element of the carrier of f
A is Element of the carrier of K
A * w is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (A,w) is Element of the carrier of V
[A,w] is set
{A,w} is set
{A} is set
{{A,w},{A}} is set
the lmult of V . [A,w] is set
x + (A * w) is Element of the carrier of V
ww is Element of the carrier of K
ww * B is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (ww,B) is Element of the carrier of f
[ww,B] is set
{ww,B} is set
{ww} is set
{{ww,B},{ww}} is set
the lmult of f . [ww,B] is set
v + (ww * B) is Element of the carrier of f
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w . ((x + (A * w)),(v + (ww * B))) is Element of the carrier of K
[(x + (A * w)),(v + (ww * B))] is set
{(x + (A * w)),(v + (ww * B))} is set
{(x + (A * w))} is set
{{(x + (A * w)),(v + (ww * B))},{(x + (A * w))}} is set
w . [(x + (A * w)),(v + (ww * B))] is set
w . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
w . [x,v] is set
w . (x,B) is Element of the carrier of K
[x,B] is set
{x,B} is set
{{x,B},{x}} is set
w . [x,B] is set
ww * (w . (x,B)) is Element of the carrier of K
(w . (x,v)) + (ww * (w . (x,B))) is Element of the carrier of K
w . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
w . [w,v] is set
A * (w . (w,v)) is Element of the carrier of K
w . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{{w,B},{w}} is set
w . [w,B] is set
ww * (w . (w,B)) is Element of the carrier of K
A * (ww * (w . (w,B))) is Element of the carrier of K
(A * (w . (w,v))) + (A * (ww * (w . (w,B)))) is Element of the carrier of K
((w . (x,v)) + (ww * (w . (x,B)))) + ((A * (w . (w,v))) + (A * (ww * (w . (w,B))))) is Element of the carrier of K
w . (x,(ww * B)) is Element of the carrier of K
[x,(ww * B)] is set
{x,(ww * B)} is set
{{x,(ww * B)},{x}} is set
w . [x,(ww * B)] is set
(w . (x,v)) + (w . (x,(ww * B))) is Element of the carrier of K
w . ((A * w),v) is Element of the carrier of K
[(A * w),v] is set
{(A * w),v} is set
{(A * w)} is set
{{(A * w),v},{(A * w)}} is set
w . [(A * w),v] is set
w . ((A * w),(ww * B)) is Element of the carrier of K
[(A * w),(ww * B)] is set
{(A * w),(ww * B)} is set
{{(A * w),(ww * B)},{(A * w)}} is set
w . [(A * w),(ww * B)] is set
(w . ((A * w),v)) + (w . ((A * w),(ww * B))) is Element of the carrier of K
((w . (x,v)) + (w . (x,(ww * B)))) + ((w . ((A * w),v)) + (w . ((A * w),(ww * B)))) is Element of the carrier of K
((w . (x,v)) + (ww * (w . (x,B)))) + ((w . ((A * w),v)) + (w . ((A * w),(ww * B)))) is Element of the carrier of K
(A * (w . (w,v))) + (w . ((A * w),(ww * B))) is Element of the carrier of K
((w . (x,v)) + (ww * (w . (x,B)))) + ((A * (w . (w,v))) + (w . ((A * w),(ww * B)))) is Element of the carrier of K
w . (w,(ww * B)) is Element of the carrier of K
[w,(ww * B)] is set
{w,(ww * B)} is set
{{w,(ww * B)},{w}} is set
w . [w,(ww * B)] is set
A * (w . (w,(ww * B))) is Element of the carrier of K
(A * (w . (w,v))) + (A * (w . (w,(ww * B)))) is Element of the carrier of K
((w . (x,v)) + (ww * (w . (x,B)))) + ((A * (w . (w,v))) + (A * (w . (w,(ww * B))))) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Element of the carrier of V
w is Element of the carrier of V
v is Element of the carrier of f
B is Element of the carrier of f
A is Element of the carrier of K
A * w is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (A,w) is Element of the carrier of V
[A,w] is set
{A,w} is set
{A} is set
{{A,w},{A}} is set
the lmult of V . [A,w] is set
x - (A * w) is Element of the carrier of V
ww is Element of the carrier of K
ww * B is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (ww,B) is Element of the carrier of f
[ww,B] is set
{ww,B} is set
{ww} is set
{{ww,B},{ww}} is set
the lmult of f . [ww,B] is set
v - (ww * B) is Element of the carrier of f
w is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
w . ((x - (A * w)),(v - (ww * B))) is Element of the carrier of K
[(x - (A * w)),(v - (ww * B))] is set
{(x - (A * w)),(v - (ww * B))} is set
{(x - (A * w))} is set
{{(x - (A * w)),(v - (ww * B))},{(x - (A * w))}} is set
w . [(x - (A * w)),(v - (ww * B))] is set
w . (x,v) is Element of the carrier of K
[x,v] is set
{x,v} is set
{x} is set
{{x,v},{x}} is set
w . [x,v] is set
w . (x,B) is Element of the carrier of K
[x,B] is set
{x,B} is set
{{x,B},{x}} is set
w . [x,B] is set
ww * (w . (x,B)) is Element of the carrier of K
(w . (x,v)) - (ww * (w . (x,B))) is Element of the carrier of K
w . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
w . [w,v] is set
A * (w . (w,v)) is Element of the carrier of K
w . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{{w,B},{w}} is set
w . [w,B] is set
ww * (w . (w,B)) is Element of the carrier of K
A * (ww * (w . (w,B))) is Element of the carrier of K
(A * (w . (w,v))) - (A * (ww * (w . (w,B)))) is Element of the carrier of K
((w . (x,v)) - (ww * (w . (x,B)))) - ((A * (w . (w,v))) - (A * (ww * (w . (w,B))))) is Element of the carrier of K
w . (x,(ww * B)) is Element of the carrier of K
[x,(ww * B)] is set
{x,(ww * B)} is set
{{x,(ww * B)},{x}} is set
w . [x,(ww * B)] is set
(w . (x,v)) - (w . (x,(ww * B))) is Element of the carrier of K
w . ((A * w),v) is Element of the carrier of K
[(A * w),v] is set
{(A * w),v} is set
{(A * w)} is set
{{(A * w),v},{(A * w)}} is set
w . [(A * w),v] is set
w . ((A * w),(ww * B)) is Element of the carrier of K
[(A * w),(ww * B)] is set
{(A * w),(ww * B)} is set
{{(A * w),(ww * B)},{(A * w)}} is set
w . [(A * w),(ww * B)] is set
(w . ((A * w),v)) - (w . ((A * w),(ww * B))) is Element of the carrier of K
((w . (x,v)) - (w . (x,(ww * B)))) - ((w . ((A * w),v)) - (w . ((A * w),(ww * B)))) is Element of the carrier of K
((w . (x,v)) - (ww * (w . (x,B)))) - ((w . ((A * w),v)) - (w . ((A * w),(ww * B)))) is Element of the carrier of K
(A * (w . (w,v))) - (w . ((A * w),(ww * B))) is Element of the carrier of K
((w . (x,v)) - (ww * (w . (x,B)))) - ((A * (w . (w,v))) - (w . ((A * w),(ww * B)))) is Element of the carrier of K
w . (w,(ww * B)) is Element of the carrier of K
[w,(ww * B)] is set
{w,(ww * B)} is set
{{w,(ww * B)},{w}} is set
w . [w,(ww * B)] is set
A * (w . (w,(ww * B))) is Element of the carrier of K
(A * (w . (w,v))) - (A * (w . (w,(ww * B)))) is Element of the carrier of K
((w . (x,v)) - (ww * (w . (x,B)))) - ((A * (w . (w,v))) - (A * (w . (w,(ww * B))))) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed doubleLoopStr
the carrier of K is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
f is non empty right_zeroed VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
dom x is Relation-like the carrier of V -defined the carrier of f -valued Element of bool [: the carrier of V, the carrier of f:]
bool [: the carrier of V, the carrier of f:] is non empty set
w is Element of the carrier of V
v is Element of the carrier of f
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
x . (w,(0. f)) is Element of the carrier of K
[w,(0. f)] is set
{w,(0. f)} is set
{{w,(0. f)},{w}} is set
x . [w,(0. f)] is set
w is Element of the carrier of V
v is Element of the carrier of f
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
x . ((0. V),v) is Element of the carrier of K
[(0. V),v] is set
{(0. V),v} is set
{(0. V)} is set
{{(0. V),v},{(0. V)}} is set
x . [(0. V),v] is set
w is set
v is set
B is Element of the carrier of V
A is Element of the carrier of f
[B,A] is Element of [: the carrier of V, the carrier of f:]
{B,A} is set
{B} is set
{{B,A},{B}} is set
ww is Element of the carrier of V
w is Element of the carrier of f
[ww,w] is Element of [: the carrier of V, the carrier of f:]
{ww,w} is set
{ww} is set
{{ww,w},{ww}} is set
x . w is set
x . (B,A) is Element of the carrier of K
[B,A] is set
x . [B,A] is set
x . (ww,w) is Element of the carrier of K
[ww,w] is set
x . [ww,w] is set
x . v is set
K is ZeroStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
bool the carrier of V is non empty set
v is set
B is Element of the carrier of V
K is ZeroStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
bool the carrier of f is non empty set
v is set
B is Element of the carrier of f
K is ZeroStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. K } is set
bool the carrier of V is non empty set
w is set
v is Element of the carrier of V
f . (v,v) is Element of the carrier of K
[v,v] is set
{v,v} is set
{v} is set
{{v,v},{v}} is set
f . [v,v] is set
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
w is Element of the carrier of f
x . ((0. V),w) is Element of the carrier of K
[(0. V),w] is set
{(0. V),w} is set
{(0. V)} is set
{{(0. V),w},{(0. V)}} is set
x . [(0. V),w] is set
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) additive 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,w) . (0. V) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
w is Element of the carrier of f
x . ((0. V),w) is Element of the carrier of K
[(0. V),w] is set
{(0. V),w} is set
{(0. V)} is set
{{(0. V),w},{(0. V)}} is set
x . [(0. V),w] is set
(K,V,f,x,w) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' x is non empty Relation-like the carrier of f -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of V, the carrier of K):]
[: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of V, the carrier of K):] is non empty set
(curry' x) . w is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
(K,V,f,x,w) . (0. V) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty right_zeroed VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
w is Element of the carrier of V
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
x . (w,(0. f)) is Element of the carrier of K
[w,(0. f)] is set
{w,(0. f)} is set
{w} is set
{{w,(0. f)},{w}} is set
x . [w,(0. f)] is set
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) additive 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,w) . (0. f) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
w is Element of the carrier of V
0. f is V56(f) Element of the carrier of f
the ZeroF of f is Element of the carrier of f
x . (w,(0. f)) is Element of the carrier of K
[w,(0. f)] is set
{w,(0. f)} is set
{w} is set
{{w,(0. f)},{w}} is set
x . [w,(0. f)] is set
(K,V,f,x,w) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry x is non empty Relation-like the carrier of V -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of f, the carrier of K):]
[: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of f, the carrier of K):] is non empty set
(curry x) . w is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
(K,V,f,x,w) . (0. f) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed doubleLoopStr
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. K } is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
f . ((0. V),(0. V)) is Element of the carrier of K
[(0. V),(0. V)] is set
{(0. V),(0. V)} is set
{(0. V)} is set
{{(0. V),(0. V)},{(0. V)}} is set
f . [(0. V),(0. V)] is set
K is non empty right_complementable add-associative right_zeroed doubleLoopStr
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. K } is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
f . ((0. V),(0. V)) is Element of the carrier of K
[(0. V),(0. V)] is set
{(0. V),(0. V)} is set
{(0. V)} is set
{{(0. V),(0. V)},{(0. V)}} is set
f . [(0. V),(0. V)] is set
K is non empty right_complementable add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. K } is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
f . ((0. V),(0. V)) is Element of the carrier of K
[(0. V),(0. V)] is set
{(0. V),(0. V)} is set
{(0. V)} is set
{{(0. V),(0. V)},{(0. V)}} is set
f . [(0. V),(0. V)] is set
K is non empty right_complementable add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. K } is set
0. V is V56(V) Element of the carrier of V
the ZeroF of V is Element of the carrier of V
f . ((0. V),(0. V)) is Element of the carrier of K
[(0. V),(0. V)] is set
{(0. V),(0. V)} is set
{(0. V)} is set
{{(0. V),(0. V)},{(0. V)}} is set
f . [(0. V),(0. V)] is set
K is ZeroStr
the carrier of K is set
V is non empty VectSpStr over K
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 K:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₁,b₂) = 0. K } is set
(K,V,f) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : f . (b₁,b₁) = 0. K } is set
(K,V,V,f) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₂,b₁) = 0. K } is set
x is set
w is Element of the carrier of V
f . (w,w) is Element of the carrier of K
[w,w] is set
{w,w} is set
{w} is set
{{w,w},{w}} is set
f . [w,w] is set
x is set
w is Element of the carrier of V
f . (w,w) is Element of the carrier of K
[w,w] is set
{w,w} is set
{w} is set
{{w,w},{w}} is set
f . [w,w] is set
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
v is Element of the carrier of V
B is Element of the carrier of V
v + B is Element of the carrier of V
A is Element of the carrier of V
ww is Element of the carrier of V
w is Element of the carrier of f
x . ((v + B),w) is Element of the carrier of K
[(v + B),w] is set
{(v + B),w} is set
{(v + B)} is set
{{(v + B),w},{(v + B)}} is set
x . [(v + B),w] is set
x . (ww,w) is Element of the carrier of K
[ww,w] is set
{ww,w} is set
{ww} is set
{{ww,w},{ww}} is set
x . [ww,w] is set
x . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{A} is set
{{A,w},{A}} is set
x . [A,w] is set
(x . (ww,w)) + (x . (A,w)) is Element of the carrier of K
(0. K) + (x . (A,w)) is Element of the carrier of K
(0. K) + (0. K) is Element of the carrier of K
v is Element of the carrier of K
B is Element of the carrier of V
v * B is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (v,B) is Element of the carrier of V
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
the lmult of V . [v,B] is set
A is Element of the carrier of V
ww is Element of the carrier of f
x . ((v * B),ww) is Element of the carrier of K
[(v * B),ww] is set
{(v * B),ww} is set
{(v * B)} is set
{{(v * B),ww},{(v * B)}} is set
x . [(v * B),ww] is set
x . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
x . [A,ww] is set
v * (x . (A,ww)) is Element of the carrier of K
v * (0. K) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
v is Element of the carrier of f
B is Element of the carrier of f
v + B is Element of the carrier of f
A is Element of the carrier of f
ww is Element of the carrier of f
w is Element of the carrier of V
x . (w,(v + B)) is Element of the carrier of K
[w,(v + B)] is set
{w,(v + B)} is set
{w} is set
{{w,(v + B)},{w}} is set
x . [w,(v + B)] is set
x . (w,ww) is Element of the carrier of K
[w,ww] is set
{w,ww} is set
{{w,ww},{w}} is set
x . [w,ww] is set
x . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{{w,A},{w}} is set
x . [w,A] is set
(x . (w,ww)) + (x . (w,A)) is Element of the carrier of K
(0. K) + (x . (w,A)) is Element of the carrier of K
(0. K) + (0. K) is Element of the carrier of K
v is Element of the carrier of K
B is Element of the carrier of f
v * B is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (v,B) is Element of the carrier of f
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
the lmult of f . [v,B] is set
A is Element of the carrier of f
ww is Element of the carrier of V
x . (ww,(v * B)) is Element of the carrier of K
[ww,(v * B)] is set
{ww,(v * B)} is set
{ww} is set
{{ww,(v * B)},{ww}} is set
x . [ww,(v * B)] is set
x . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{{ww,A},{ww}} is set
x . [ww,A] is set
v * (x . (ww,A)) is Element of the carrier of K
v * (0. K) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
w is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of w is non empty set
v is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of v is non empty set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
w is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
the carrier of w is non empty set
v is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
the carrier of v is non empty set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
CosetSet (V,(K,V,f,x)) is non empty Element of bool (bool the carrier of V)
bool the carrier of V is non empty set
bool (bool the carrier of V) is non empty set
addCoset (V,(K,V,f,x)) is non empty Relation-like [:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):] -defined CosetSet (V,(K,V,f,x)) -valued Function-like V20([:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):]) V21([:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):], CosetSet (V,(K,V,f,x))) Element of bool [:[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):]
[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):] is non empty set
[:[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
bool [:[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
lmultCoset (V,(K,V,f,x)) is non empty Relation-like [: the carrier of K,(CosetSet (V,(K,V,f,x))):] -defined CosetSet (V,(K,V,f,x)) -valued Function-like V20([: the carrier of K,(CosetSet (V,(K,V,f,x))):]) V21([: the carrier of K,(CosetSet (V,(K,V,f,x))):], CosetSet (V,(K,V,f,x))) Element of bool [:[: the carrier of K,(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):]
[: the carrier of K,(CosetSet (V,(K,V,f,x))):] is non empty set
[:[: the carrier of K,(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K,(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
A is Element of the carrier of V
A + (K,V,f,x) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
v is Element of the carrier of f
x . (A,v) is Element of the carrier of K
[A,v] is set
{A,v} is set
{A} is set
{{A,v},{A}} is set
x . [A,v] is set
w is Element of the carrier of V
w + (K,V,f,x) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
v is Element of the carrier of V
w + v is Element of the carrier of V
the carrier of (K,V,f,x) is non empty set
(K,V,f,x) is non empty Element of bool the carrier of V
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
B is Element of the carrier of K
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
x . (v,v) is Element of the carrier of K
[v,v] is set
{v,v} is set
{v} is set
{{v,v},{v}} is set
x . [v,v] is set
(x . (w,v)) + (x . (v,v)) is Element of the carrier of K
(x . (w,v)) + (0. K) is Element of the carrier of K
w is Element of the carrier of V
w is Element of the carrier of V
w + (K,V,f,x) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
x . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
w is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
v is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
A is Element of the carrier of f
(K,(VectQuot (V,(K,V,f,x))),f,v,A) is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:]
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:] is non empty set
K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) is non empty functional M5( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)
curry' v is non empty Relation-like the carrier of f -defined K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):]
[: the carrier of f,K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):] is non empty set
bool [: the carrier of f,K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):] is non empty set
(curry' v) . A is Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of V
w + (K,V,f,x) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of V
v + (K,V,f,x) is Element of bool the carrier of V
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
the addF of (VectQuot (V,(K,V,f,x))) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):] -defined the carrier of (VectQuot (V,(K,V,f,x))) -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):]
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
(addCoset (V,(K,V,f,x))) . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(addCoset (V,(K,V,f,x))) . [w,v] is set
w + v is Element of the carrier of V
(w + v) + (K,V,f,x) is Element of bool the carrier of V
{ ((w + v) + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
w + v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),f,v,A) . (w + v) is Element of the carrier of K
v . ((w + v),A) is Element of the carrier of K
[(w + v),A] is set
{(w + v),A} is set
{(w + v)} is set
{{(w + v),A},{(w + v)}} is set
v . [(w + v),A] is set
x . ((w + v),A) is Element of the carrier of K
[(w + v),A] is set
{(w + v),A} is set
{(w + v)} is set
{{(w + v),A},{(w + v)}} is set
x . [(w + v),A] is set
x . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{w} is set
{{w,A},{w}} is set
x . [w,A] is set
x . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{v} is set
{{v,A},{v}} is set
x . [v,A] is set
(x . (w,A)) + (x . (v,A)) is Element of the carrier of K
v . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{{w,A},{w}} is set
v . [w,A] is set
(v . (w,A)) + (x . (v,A)) is Element of the carrier of K
v . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{v} is set
{{v,A},{v}} is set
v . [v,A] is set
(v . (w,A)) + (v . (v,A)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),f,v,A) . w is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),f,v,A) . w) + (v . (v,A)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),f,v,A) . v is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),f,v,A) . w) + ((K,(VectQuot (V,(K,V,f,x))),f,v,A) . v) is Element of the carrier of K
A is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
B is Element of the carrier of f
(K,(VectQuot (V,(K,V,f,x))),f,A,B) is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) additive 0-preserving Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:]
curry' A is non empty Relation-like the carrier of f -defined K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) -valued Function-like V20( the carrier of f) V21( the carrier of f,K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)) Element of bool [: the carrier of f,K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):]
(curry' A) . B is Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of V
v + (K,V,f,x) is Element of bool the carrier of V
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
the lmult of (VectQuot (V,(K,V,f,x))) is non empty Relation-like [: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):] -defined the carrier of (VectQuot (V,(K,V,f,x))) -valued Function-like V20([: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):]) V21([: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x)))) Element of bool [:[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):]
[:[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
w is Element of the carrier of K
(lmultCoset (V,(K,V,f,x))) . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(lmultCoset (V,(K,V,f,x))) . [w,v] is set
w * v is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (w,v) is Element of the carrier of V
[w,v] is set
{w,v} is set
{{w,v},{w}} is set
the lmult of V . [w,v] is set
(w * v) + (K,V,f,x) is Element of bool the carrier of V
{ ((w * v) + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
w * v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
the lmult of (VectQuot (V,(K,V,f,x))) . (w,v) is Element of the carrier of (VectQuot (V,(K,V,f,x)))
the lmult of (VectQuot (V,(K,V,f,x))) . [w,v] is set
(K,(VectQuot (V,(K,V,f,x))),f,A,B) . (w * v) is Element of the carrier of K
A . ((w * v),B) is Element of the carrier of K
[(w * v),B] is set
{(w * v),B} is set
{(w * v)} is set
{{(w * v),B},{(w * v)}} is set
A . [(w * v),B] is set
x . ((w * v),B) is Element of the carrier of K
[(w * v),B] is set
{(w * v),B} is set
{(w * v)} is set
{{(w * v),B},{(w * v)}} is set
x . [(w * v),B] is set
x . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
x . [v,B] is set
w * (x . (v,B)) is Element of the carrier of K
A . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
A . [v,B] is set
w * (A . (v,B)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),f,A,B) . v is Element of the carrier of K
w * ((K,(VectQuot (V,(K,V,f,x))),f,A,B) . v) is Element of the carrier of K
B is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of V
w + (K,V,f,x) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
v is Element of the carrier of f
B . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
B . [w,v] is set
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
B is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
A is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
ww is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of V
v + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
w is Element of the carrier of f
B . (ww,w) is Element of the carrier of K
[ww,w] is set
{ww,w} is set
{ww} is set
{{ww,w},{ww}} is set
B . [ww,w] is set
x . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
x . [v,w] is set
A . (ww,w) is Element of the carrier of K
A . [ww,w] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
CosetSet (f,(K,V,f,x)) is non empty Element of bool (bool the carrier of f)
bool the carrier of f is non empty set
bool (bool the carrier of f) is non empty set
addCoset (f,(K,V,f,x)) is non empty Relation-like [:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):] -defined CosetSet (f,(K,V,f,x)) -valued Function-like V20([:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):]) V21([:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):], CosetSet (f,(K,V,f,x))) Element of bool [:[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):]
[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):] is non empty set
[:[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
bool [:[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
lmultCoset (f,(K,V,f,x)) is non empty Relation-like [: the carrier of K,(CosetSet (f,(K,V,f,x))):] -defined CosetSet (f,(K,V,f,x)) -valued Function-like V20([: the carrier of K,(CosetSet (f,(K,V,f,x))):]) V21([: the carrier of K,(CosetSet (f,(K,V,f,x))):], CosetSet (f,(K,V,f,x))) Element of bool [:[: the carrier of K,(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):]
[: the carrier of K,(CosetSet (f,(K,V,f,x))):] is non empty set
[:[: the carrier of K,(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K,(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
A is Element of the carrier of f
A + (K,V,f,x) is Element of bool the carrier of f
{ (A + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
w is Element of the carrier of V
x . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{w} is set
{{w,A},{w}} is set
x . [w,A] is set
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v is Element of the carrier of f
w + v is Element of the carrier of f
the carrier of (K,V,f,x) is non empty set
(K,V,f,x) is non empty Element of bool the carrier of f
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
B is Element of the carrier of K
x . (w,w) is Element of the carrier of K
[w,w] is set
{w,w} is set
{{w,w},{w}} is set
x . [w,w] is set
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{{w,v},{w}} is set
x . [w,v] is set
(x . (w,w)) + (x . (w,v)) is Element of the carrier of K
(x . (w,w)) + (0. K) is Element of the carrier of K
w is Element of the carrier of f
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
x . (w,w) is set
[w,w] is set
{w,w} is set
{{w,w},{w}} is set
x . [w,w] is set
w is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
v is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
A is Element of the carrier of V
(K,V,(VectQuot (f,(K,V,f,x))),v,A) is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:]
[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:] is non empty set
K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) is non empty functional M5( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)
curry v is non empty Relation-like the carrier of V -defined K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):]
[: the carrier of V,K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):] is non empty set
bool [: the carrier of V,K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):] is non empty set
(curry v) . A is Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
v is Element of the carrier of f
v + (K,V,f,x) is Element of bool the carrier of f
{ (v + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
the addF of (VectQuot (f,(K,V,f,x))) is non empty Relation-like [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of (VectQuot (f,(K,V,f,x))) -valued Function-like V20([: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):]
[:[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
bool [:[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
(addCoset (f,(K,V,f,x))) . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(addCoset (f,(K,V,f,x))) . [w,v] is set
w + v is Element of the carrier of f
(w + v) + (K,V,f,x) is Element of bool the carrier of f
{ ((w + v) + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
w + v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,(VectQuot (f,(K,V,f,x))),v,A) . (w + v) is Element of the carrier of K
v . (A,(w + v)) is Element of the carrier of K
[A,(w + v)] is set
{A,(w + v)} is set
{A} is set
{{A,(w + v)},{A}} is set
v . [A,(w + v)] is set
x . (A,(w + v)) is Element of the carrier of K
[A,(w + v)] is set
{A,(w + v)} is set
{{A,(w + v)},{A}} is set
x . [A,(w + v)] is set
x . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{{A,w},{A}} is set
x . [A,w] is set
x . (A,v) is Element of the carrier of K
[A,v] is set
{A,v} is set
{{A,v},{A}} is set
x . [A,v] is set
(x . (A,w)) + (x . (A,v)) is Element of the carrier of K
v . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{{A,w},{A}} is set
v . [A,w] is set
(v . (A,w)) + (x . (A,v)) is Element of the carrier of K
v . (A,v) is Element of the carrier of K
[A,v] is set
{A,v} is set
{{A,v},{A}} is set
v . [A,v] is set
(v . (A,w)) + (v . (A,v)) is Element of the carrier of K
(K,V,(VectQuot (f,(K,V,f,x))),v,A) . w is Element of the carrier of K
((K,V,(VectQuot (f,(K,V,f,x))),v,A) . w) + (v . (A,v)) is Element of the carrier of K
(K,V,(VectQuot (f,(K,V,f,x))),v,A) . v is Element of the carrier of K
((K,V,(VectQuot (f,(K,V,f,x))),v,A) . w) + ((K,V,(VectQuot (f,(K,V,f,x))),v,A) . v) is Element of the carrier of K
A is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
B is Element of the carrier of V
(K,V,(VectQuot (f,(K,V,f,x))),A,B) is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) additive 0-preserving Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:]
curry A is non empty Relation-like the carrier of V -defined K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) -valued Function-like V20( the carrier of V) V21( the carrier of V,K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)) Element of bool [: the carrier of V,K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):]
(curry A) . B is Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
v is Element of the carrier of f
v + (K,V,f,x) is Element of bool the carrier of f
{ (v + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
the lmult of (VectQuot (f,(K,V,f,x))) is non empty Relation-like [: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of (VectQuot (f,(K,V,f,x))) -valued Function-like V20([: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x)))) Element of bool [:[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):]
[:[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
w is Element of the carrier of K
(lmultCoset (f,(K,V,f,x))) . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(lmultCoset (f,(K,V,f,x))) . [w,v] is set
w * v is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (w,v) is Element of the carrier of f
[w,v] is set
{w,v} is set
{{w,v},{w}} is set
the lmult of f . [w,v] is set
(w * v) + (K,V,f,x) is Element of bool the carrier of f
{ ((w * v) + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
w * v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
the lmult of (VectQuot (f,(K,V,f,x))) . (w,v) is Element of the carrier of (VectQuot (f,(K,V,f,x)))
the lmult of (VectQuot (f,(K,V,f,x))) . [w,v] is set
(K,V,(VectQuot (f,(K,V,f,x))),A,B) . (w * v) is Element of the carrier of K
A . (B,(w * v)) is Element of the carrier of K
[B,(w * v)] is set
{B,(w * v)} is set
{B} is set
{{B,(w * v)},{B}} is set
A . [B,(w * v)] is set
x . (B,(w * v)) is Element of the carrier of K
[B,(w * v)] is set
{B,(w * v)} is set
{{B,(w * v)},{B}} is set
x . [B,(w * v)] is set
x . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{{B,v},{B}} is set
x . [B,v] is set
w * (x . (B,v)) is Element of the carrier of K
A . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{{B,v},{B}} is set
A . [B,v] is set
w * (A . (B,v)) is Element of the carrier of K
(K,V,(VectQuot (f,(K,V,f,x))),A,B) . v is Element of the carrier of K
w * ((K,V,(VectQuot (f,(K,V,f,x))),A,B) . v) is Element of the carrier of K
B is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v is Element of the carrier of V
B . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
B . [v,w] is set
x . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{{v,w},{v}} is set
x . [v,w] is set
B is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
A is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
v is Element of the carrier of f
v + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (v + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
ww is Element of the carrier of V
B . (ww,w) is Element of the carrier of K
[ww,w] is set
{ww,w} is set
{ww} is set
{{ww,w},{ww}} is set
B . [ww,w] is set
x . (ww,v) is Element of the carrier of K
[ww,v] is set
{ww,v} is set
{{ww,v},{ww}} is set
x . [ww,v] is set
A . (ww,w) is Element of the carrier of K
A . [ww,w] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x) is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K):]
[: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
A is Element of the carrier of V
A + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
ww is Element of the carrier of f
w is Element of the carrier of f
ww + w is Element of the carrier of f
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . (ww + w) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . ww is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . w is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . ww) + ((K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . w) is Element of the carrier of K
ww + w is Element of the carrier of f
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . (ww + w) is Element of the carrier of K
(K,V,f,x) . (v,(ww + w)) is Element of the carrier of K
[v,(ww + w)] is set
{v,(ww + w)} is set
{v} is set
{{v,(ww + w)},{v}} is set
(K,V,f,x) . [v,(ww + w)] is set
x . (A,(ww + w)) is Element of the carrier of K
[A,(ww + w)] is set
{A,(ww + w)} is set
{A} is set
{{A,(ww + w)},{A}} is set
x . [A,(ww + w)] is set
x . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{{A,ww},{A}} is set
x . [A,ww] is set
x . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{{A,w},{A}} is set
x . [A,w] is set
(x . (A,ww)) + (x . (A,w)) is Element of the carrier of K
(K,V,f,x) . (v,ww) is Element of the carrier of K
[v,ww] is set
{v,ww} is set
{{v,ww},{v}} is set
(K,V,f,x) . [v,ww] is set
((K,V,f,x) . (v,ww)) + (x . (A,w)) is Element of the carrier of K
(K,V,f,x) . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{{v,w},{v}} is set
(K,V,f,x) . [v,w] is set
((K,V,f,x) . (v,ww)) + ((K,V,f,x) . (v,w)) is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . ww) + ((K,V,f,x) . (v,w)) is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . ww) + ((K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . w) is Element of the carrier of K
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
K116( the carrier of f, the carrier of K) is non empty functional M5( the carrier of f, the carrier of K)
curry (K,V,f,x) is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined K116( the carrier of f, the carrier of K) -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K)) Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K):]
[: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K):] is non empty set
bool [: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of f, the carrier of K):] is non empty set
(curry (K,V,f,x)) . v is Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of K116( the carrier of f, the carrier of K)
A is Element of the carrier of V
A + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
ww is Element of the carrier of f
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . ww is Element of the carrier of K
w is Element of the carrier of K
w * ww is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (w,ww) is Element of the carrier of f
[w,ww] is set
{w,ww} is set
{w} is set
{{w,ww},{w}} is set
the lmult of f . [w,ww] is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . (w * ww) is Element of the carrier of K
w * ((K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x),v) . ww) is Element of the carrier of K
(K,V,f,x) . (v,(w * ww)) is Element of the carrier of K
[v,(w * ww)] is set
{v,(w * ww)} is set
{v} is set
{{v,(w * ww)},{v}} is set
(K,V,f,x) . [v,(w * ww)] is set
x . (A,(w * ww)) is Element of the carrier of K
[A,(w * ww)] is set
{A,(w * ww)} is set
{A} is set
{{A,(w * ww)},{A}} is set
x . [A,(w * ww)] is set
x . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{{A,ww},{A}} is set
x . [A,ww] is set
w * (x . (A,ww)) is Element of the carrier of K
(K,V,f,x) . (v,ww) is Element of the carrier of K
[v,ww] is set
{v,ww} is set
{{v,ww},{v}} is set
(K,V,f,x) . [v,ww] is set
w * ((K,V,f,x) . (v,ww)) is Element of the carrier of K
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x) is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K):]
[: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
A is Element of the carrier of f
A + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (A + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
ww is Element of the carrier of V
w is Element of the carrier of V
ww + w is Element of the carrier of V
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . (ww + w) is Element of the carrier of K
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . ww is Element of the carrier of K
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . w is Element of the carrier of K
((K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . ww) + ((K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . w) is Element of the carrier of K
ww + w is Element of the carrier of V
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . (ww + w) is Element of the carrier of K
(K,V,f,x) . ((ww + w),v) is Element of the carrier of K
[(ww + w),v] is set
{(ww + w),v} is set
{(ww + w)} is set
{{(ww + w),v},{(ww + w)}} is set
(K,V,f,x) . [(ww + w),v] is set
x . ((ww + w),A) is Element of the carrier of K
[(ww + w),A] is set
{(ww + w),A} is set
{{(ww + w),A},{(ww + w)}} is set
x . [(ww + w),A] is set
x . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
x . [ww,A] is set
x . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{w} is set
{{w,A},{w}} is set
x . [w,A] is set
(x . (ww,A)) + (x . (w,A)) is Element of the carrier of K
(K,V,f,x) . (ww,v) is Element of the carrier of K
[ww,v] is set
{ww,v} is set
{{ww,v},{ww}} is set
(K,V,f,x) . [ww,v] is set
((K,V,f,x) . (ww,v)) + (x . (w,A)) is Element of the carrier of K
(K,V,f,x) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{{w,v},{w}} is set
(K,V,f,x) . [w,v] is set
((K,V,f,x) . (ww,v)) + ((K,V,f,x) . (w,v)) is Element of the carrier of K
((K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . ww) + ((K,V,f,x) . (w,v)) is Element of the carrier of K
((K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . ww) + ((K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . w) is Element of the carrier of K
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
K116( the carrier of V, the carrier of K) is non empty functional M5( the carrier of V, the carrier of K)
curry' (K,V,f,x) is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined K116( the carrier of V, the carrier of K) -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K)) Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K):]
[: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K):] is non empty set
bool [: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of V, the carrier of K):] is non empty set
(curry' (K,V,f,x)) . v is Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of K116( the carrier of V, the carrier of K)
A is Element of the carrier of f
A + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (A + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
ww is Element of the carrier of V
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . ww is Element of the carrier of K
w is Element of the carrier of K
w * ww is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (w,ww) is Element of the carrier of V
[w,ww] is set
{w,ww} is set
{w} is set
{{w,ww},{w}} is set
the lmult of V . [w,ww] is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . (w * ww) is Element of the carrier of K
w * ((K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x),v) . ww) is Element of the carrier of K
(K,V,f,x) . ((w * ww),v) is Element of the carrier of K
[(w * ww),v] is set
{(w * ww),v} is set
{(w * ww)} is set
{{(w * ww),v},{(w * ww)}} is set
(K,V,f,x) . [(w * ww),v] is set
x . ((w * ww),A) is Element of the carrier of K
[(w * ww),A] is set
{(w * ww),A} is set
{{(w * ww),A},{(w * ww)}} is set
x . [(w * ww),A] is set
x . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
x . [ww,A] is set
w * (x . (ww,A)) is Element of the carrier of K
(K,V,f,x) . (ww,v) is Element of the carrier of K
[ww,v] is set
{ww,v} is set
{{ww,v},{ww}} is set
(K,V,f,x) . [ww,v] is set
w * ((K,V,f,x) . (ww,v)) is Element of the carrier of K
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
CosetSet (V,(K,V,f,x)) is non empty Element of bool (bool the carrier of V)
bool the carrier of V is non empty set
bool (bool the carrier of V) is non empty set
addCoset (V,(K,V,f,x)) is non empty Relation-like [:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):] -defined CosetSet (V,(K,V,f,x)) -valued Function-like V20([:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):]) V21([:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):], CosetSet (V,(K,V,f,x))) Element of bool [:[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):]
[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):] is non empty set
[:[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
bool [:[:(CosetSet (V,(K,V,f,x))),(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
lmultCoset (V,(K,V,f,x)) is non empty Relation-like [: the carrier of K,(CosetSet (V,(K,V,f,x))):] -defined CosetSet (V,(K,V,f,x)) -valued Function-like V20([: the carrier of K,(CosetSet (V,(K,V,f,x))):]) V21([: the carrier of K,(CosetSet (V,(K,V,f,x))):], CosetSet (V,(K,V,f,x))) Element of bool [:[: the carrier of K,(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):]
[: the carrier of K,(CosetSet (V,(K,V,f,x))):] is non empty set
[:[: the carrier of K,(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K,(CosetSet (V,(K,V,f,x))):],(CosetSet (V,(K,V,f,x))):] is non empty set
CosetSet (f,(K,V,f,x)) is non empty Element of bool (bool the carrier of f)
bool the carrier of f is non empty set
bool (bool the carrier of f) is non empty set
addCoset (f,(K,V,f,x)) is non empty Relation-like [:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):] -defined CosetSet (f,(K,V,f,x)) -valued Function-like V20([:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):]) V21([:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):], CosetSet (f,(K,V,f,x))) Element of bool [:[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):]
[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):] is non empty set
[:[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
bool [:[:(CosetSet (f,(K,V,f,x))),(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
lmultCoset (f,(K,V,f,x)) is non empty Relation-like [: the carrier of K,(CosetSet (f,(K,V,f,x))):] -defined CosetSet (f,(K,V,f,x)) -valued Function-like V20([: the carrier of K,(CosetSet (f,(K,V,f,x))):]) V21([: the carrier of K,(CosetSet (f,(K,V,f,x))):], CosetSet (f,(K,V,f,x))) Element of bool [:[: the carrier of K,(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):]
[: the carrier of K,(CosetSet (f,(K,V,f,x))):] is non empty set
[:[: the carrier of K,(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K,(CosetSet (f,(K,V,f,x))):],(CosetSet (f,(K,V,f,x))):] is non empty set
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of V
v + (K,V,f,x) is Element of bool the carrier of V
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
c₁₈ is Element of the carrier of f
c₁₈ + (K,V,f,x) is Element of bool the carrier of f
{ (c₁₈ + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
x . (v,c₁₈) is Element of the carrier of K
[v,c₁₈] is set
{v,c₁₈} is set
{v} is set
{{v,c₁₈},{v}} is set
x . [v,c₁₈] is set
A is Element of the carrier of V
A + (K,V,f,x) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
a is Element of the carrier of V
A + a is Element of the carrier of V
the carrier of (K,V,f,x) is non empty set
(K,V,f,x) is non empty Element of bool the carrier of V
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
B is Element of the carrier of f
B + (K,V,f,x) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
b is Element of the carrier of f
B + b is Element of the carrier of f
the carrier of (K,V,f,x) is non empty set
(K,V,f,x) is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
ffv is Element of the carrier of K
x . (A,B) is Element of the carrier of K
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
x . [A,B] is set
x . (A,b) is Element of the carrier of K
[A,b] is set
{A,b} is set
{{A,b},{A}} is set
x . [A,b] is set
(x . (A,B)) + (x . (A,b)) is Element of the carrier of K
x . (a,B) is Element of the carrier of K
[a,B] is set
{a,B} is set
{a} is set
{{a,B},{a}} is set
x . [a,B] is set
x . (a,b) is Element of the carrier of K
[a,b] is set
{a,b} is set
{{a,b},{a}} is set
x . [a,b] is set
(x . (a,B)) + (x . (a,b)) is Element of the carrier of K
((x . (A,B)) + (x . (A,b))) + ((x . (a,B)) + (x . (a,b))) is Element of the carrier of K
(x . (A,B)) + (0. K) is Element of the carrier of K
((x . (A,B)) + (0. K)) + ((x . (a,B)) + (x . (a,b))) is Element of the carrier of K
(0. K) + (x . (a,b)) is Element of the carrier of K
((x . (A,B)) + (0. K)) + ((0. K) + (x . (a,b))) is Element of the carrier of K
(x . (A,B)) + ((0. K) + (x . (a,b))) is Element of the carrier of K
(x . (A,B)) + (x . (a,b)) is Element of the carrier of K
c₂₄ is Element of the carrier of f
c₂₄ is Element of the carrier of V
c₂₄ is Element of the carrier of V
A is Element of the carrier of V
A + (K,V,f,x) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
B is Element of the carrier of f
B + (K,V,f,x) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
x . (A,B) is Element of the carrier of K
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
x . [A,B] is set
v is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
c₁₈ is Element of the carrier of f
c₁₈ + (K,V,f,x) is Element of bool the carrier of f
{ (c₁₈ + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
w is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:]
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:] is non empty set
K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) is non empty functional M5( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)
curry' w is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)) Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):]
[: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):] is non empty set
bool [: the carrier of (VectQuot (f,(K,V,f,x))),K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K):] is non empty set
(curry' w) . v is Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)
A is Element of the carrier of (VectQuot (V,(K,V,f,x)))
a is Element of the carrier of V
a + (K,V,f,x) is Element of bool the carrier of V
{ (a + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
the lmult of (VectQuot (V,(K,V,f,x))) is non empty Relation-like [: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):] -defined the carrier of (VectQuot (V,(K,V,f,x))) -valued Function-like V20([: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):]) V21([: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x)))) Element of bool [:[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):]
[:[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K, the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
B is Element of the carrier of K
(lmultCoset (V,(K,V,f,x))) . (B,A) is set
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(lmultCoset (V,(K,V,f,x))) . [B,A] is set
B * a is Element of the carrier of V
the lmult of V is non empty Relation-like [: the carrier of K, the carrier of V:] -defined the carrier of V -valued Function-like V20([: the carrier of K, the carrier of V:]) V21([: the carrier of K, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of K, the carrier of V:], the carrier of V:]
[: the carrier of K, the carrier of V:] is non empty set
[:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of K, the carrier of V:], the carrier of V:] is non empty set
the lmult of V . (B,a) is Element of the carrier of V
[B,a] is set
{B,a} is set
{{B,a},{B}} is set
the lmult of V . [B,a] is set
(B * a) + (K,V,f,x) is Element of bool the carrier of V
{ ((B * a) + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
B * A is Element of the carrier of (VectQuot (V,(K,V,f,x)))
the lmult of (VectQuot (V,(K,V,f,x))) . (B,A) is Element of the carrier of (VectQuot (V,(K,V,f,x)))
the lmult of (VectQuot (V,(K,V,f,x))) . [B,A] is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . (B * A) is Element of the carrier of K
w . ((B * A),v) is Element of the carrier of K
[(B * A),v] is set
{(B * A),v} is set
{(B * A)} is set
{{(B * A),v},{(B * A)}} is set
w . [(B * A),v] is set
x . ((B * a),c₁₈) is Element of the carrier of K
[(B * a),c₁₈] is set
{(B * a),c₁₈} is set
{(B * a)} is set
{{(B * a),c₁₈},{(B * a)}} is set
x . [(B * a),c₁₈] is set
x . (a,c₁₈) is Element of the carrier of K
[a,c₁₈] is set
{a,c₁₈} is set
{a} is set
{{a,c₁₈},{a}} is set
x . [a,c₁₈] is set
B * (x . (a,c₁₈)) is Element of the carrier of K
w . (A,v) is Element of the carrier of K
[A,v] is set
{A,v} is set
{A} is set
{{A,v},{A}} is set
w . [A,v] is set
B * (w . (A,v)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A is Element of the carrier of K
B * ((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A) is Element of the carrier of K
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
c₁₈ is Element of the carrier of V
c₁₈ + (K,V,f,x) is Element of bool the carrier of V
{ (c₁₈ + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:]
[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:] is non empty set
K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) is non empty functional M5( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)
curry w is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)) Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):]
[: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):] is non empty set
bool [: the carrier of (VectQuot (V,(K,V,f,x))),K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K):] is non empty set
(curry w) . v is Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)
A is Element of the carrier of (VectQuot (f,(K,V,f,x)))
a is Element of the carrier of f
a + (K,V,f,x) is Element of bool the carrier of f
{ (a + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
the lmult of (VectQuot (f,(K,V,f,x))) is non empty Relation-like [: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of (VectQuot (f,(K,V,f,x))) -valued Function-like V20([: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x)))) Element of bool [:[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):]
[:[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
bool [:[: the carrier of K, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
B is Element of the carrier of K
(lmultCoset (f,(K,V,f,x))) . (B,A) is set
[B,A] is set
{B,A} is set
{B} is set
{{B,A},{B}} is set
(lmultCoset (f,(K,V,f,x))) . [B,A] is set
B * a is Element of the carrier of f
the lmult of f is non empty Relation-like [: the carrier of K, the carrier of f:] -defined the carrier of f -valued Function-like V20([: the carrier of K, the carrier of f:]) V21([: the carrier of K, the carrier of f:], the carrier of f) Element of bool [:[: the carrier of K, the carrier of f:], the carrier of f:]
[: the carrier of K, the carrier of f:] is non empty set
[:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
bool [:[: the carrier of K, the carrier of f:], the carrier of f:] is non empty set
the lmult of f . (B,a) is Element of the carrier of f
[B,a] is set
{B,a} is set
{{B,a},{B}} is set
the lmult of f . [B,a] is set
(B * a) + (K,V,f,x) is Element of bool the carrier of f
{ ((B * a) + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
B * A is Element of the carrier of (VectQuot (f,(K,V,f,x)))
the lmult of (VectQuot (f,(K,V,f,x))) . (B,A) is Element of the carrier of (VectQuot (f,(K,V,f,x)))
the lmult of (VectQuot (f,(K,V,f,x))) . [B,A] is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . (B * A) is Element of the carrier of K
w . (v,(B * A)) is Element of the carrier of K
[v,(B * A)] is set
{v,(B * A)} is set
{v} is set
{{v,(B * A)},{v}} is set
w . [v,(B * A)] is set
x . (c₁₈,(B * a)) is Element of the carrier of K
[c₁₈,(B * a)] is set
{c₁₈,(B * a)} is set
{c₁₈} is set
{{c₁₈,(B * a)},{c₁₈}} is set
x . [c₁₈,(B * a)] is set
x . (c₁₈,a) is Element of the carrier of K
[c₁₈,a] is set
{c₁₈,a} is set
{{c₁₈,a},{c₁₈}} is set
x . [c₁₈,a] is set
B * (x . (c₁₈,a)) is Element of the carrier of K
w . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{{v,A},{v}} is set
w . [v,A] is set
B * (w . (v,A)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A is Element of the carrier of K
B * ((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A) is Element of the carrier of K
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
c₁₈ is Element of the carrier of f
c₁₈ + (K,V,f,x) is Element of bool the carrier of f
{ (c₁₈ + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) is non empty Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K:]
(curry' w) . v is Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(K,V,f,x)))) V21( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (V,(K,V,f,x))), the carrier of K)
A is Element of the carrier of (VectQuot (V,(K,V,f,x)))
a is Element of the carrier of V
a + (K,V,f,x) is Element of bool the carrier of V
{ (a + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
B is Element of the carrier of (VectQuot (V,(K,V,f,x)))
b is Element of the carrier of V
b + (K,V,f,x) is Element of bool the carrier of V
{ (b + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
the addF of (VectQuot (V,(K,V,f,x))) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):] -defined the carrier of (VectQuot (V,(K,V,f,x))) -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):]
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (V,(K,V,f,x))):], the carrier of (VectQuot (V,(K,V,f,x))):] is non empty set
(addCoset (V,(K,V,f,x))) . (A,B) is set
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
(addCoset (V,(K,V,f,x))) . [A,B] is set
a + b is Element of the carrier of V
(a + b) + (K,V,f,x) is Element of bool the carrier of V
{ ((a + b) + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
A + B is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . (A + B) is Element of the carrier of K
w . ((A + B),v) is Element of the carrier of K
[(A + B),v] is set
{(A + B),v} is set
{(A + B)} is set
{{(A + B),v},{(A + B)}} is set
w . [(A + B),v] is set
x . ((a + b),c₁₈) is Element of the carrier of K
[(a + b),c₁₈] is set
{(a + b),c₁₈} is set
{(a + b)} is set
{{(a + b),c₁₈},{(a + b)}} is set
x . [(a + b),c₁₈] is set
x . (a,c₁₈) is Element of the carrier of K
[a,c₁₈] is set
{a,c₁₈} is set
{a} is set
{{a,c₁₈},{a}} is set
x . [a,c₁₈] is set
x . (b,c₁₈) is Element of the carrier of K
[b,c₁₈] is set
{b,c₁₈} is set
{b} is set
{{b,c₁₈},{b}} is set
x . [b,c₁₈] is set
(x . (a,c₁₈)) + (x . (b,c₁₈)) is Element of the carrier of K
w . (A,v) is Element of the carrier of K
[A,v] is set
{A,v} is set
{{A,v},{A}} is set
w . [A,v] is set
(w . (A,v)) + (x . (b,c₁₈)) is Element of the carrier of K
w . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{B} is set
{{B,v},{B}} is set
w . [B,v] is set
(w . (A,v)) + (w . (B,v)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A) + (w . (B,v)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . B is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A) + ((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . B) is Element of the carrier of K
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
c₁₈ is Element of the carrier of V
c₁₈ + (K,V,f,x) is Element of bool the carrier of V
{ (c₁₈ + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) is non empty Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of bool [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K:]
(curry w) . v is Relation-like the carrier of (VectQuot (f,(K,V,f,x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(K,V,f,x)))) V21( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K) Element of K116( the carrier of (VectQuot (f,(K,V,f,x))), the carrier of K)
A is Element of the carrier of (VectQuot (f,(K,V,f,x)))
a is Element of the carrier of f
a + (K,V,f,x) is Element of bool the carrier of f
{ (a + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
B is Element of the carrier of (VectQuot (f,(K,V,f,x)))
b is Element of the carrier of f
b + (K,V,f,x) is Element of bool the carrier of f
{ (b + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
the addF of (VectQuot (f,(K,V,f,x))) is non empty Relation-like [: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of (VectQuot (f,(K,V,f,x))) -valued Function-like V20([: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):]
[:[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
bool [:[: the carrier of (VectQuot (f,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
(addCoset (f,(K,V,f,x))) . (A,B) is set
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
(addCoset (f,(K,V,f,x))) . [A,B] is set
a + b is Element of the carrier of f
(a + b) + (K,V,f,x) is Element of bool the carrier of f
{ ((a + b) + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
A + B is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . (A + B) is Element of the carrier of K
w . (v,(A + B)) is Element of the carrier of K
[v,(A + B)] is set
{v,(A + B)} is set
{v} is set
{{v,(A + B)},{v}} is set
w . [v,(A + B)] is set
x . (c₁₈,(a + b)) is Element of the carrier of K
[c₁₈,(a + b)] is set
{c₁₈,(a + b)} is set
{c₁₈} is set
{{c₁₈,(a + b)},{c₁₈}} is set
x . [c₁₈,(a + b)] is set
x . (c₁₈,a) is Element of the carrier of K
[c₁₈,a] is set
{c₁₈,a} is set
{{c₁₈,a},{c₁₈}} is set
x . [c₁₈,a] is set
x . (c₁₈,b) is Element of the carrier of K
[c₁₈,b] is set
{c₁₈,b} is set
{{c₁₈,b},{c₁₈}} is set
x . [c₁₈,b] is set
(x . (c₁₈,a)) + (x . (c₁₈,b)) is Element of the carrier of K
w . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{{v,A},{v}} is set
w . [v,A] is set
(w . (v,A)) + (x . (c₁₈,b)) is Element of the carrier of K
w . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{{v,B},{v}} is set
w . [v,B] is set
(w . (v,A)) + (w . (v,B)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A) + (w . (v,B)) is Element of the carrier of K
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . B is Element of the carrier of K
((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . A) + ((K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),w,v) . B) is Element of the carrier of K
v is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
c₁₈ is Element of the carrier of (VectQuot (V,(K,V,f,x)))
A is Element of the carrier of V
A + (K,V,f,x) is Element of bool the carrier of V
{ (A + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
ffv is Element of the carrier of (VectQuot (f,(K,V,f,x)))
B is Element of the carrier of f
B + (K,V,f,x) is Element of bool the carrier of f
{ (B + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v . (c₁₈,ffv) is Element of the carrier of K
[c₁₈,ffv] is set
{c₁₈,ffv} is set
{c₁₈} is set
{{c₁₈,ffv},{c₁₈}} is set
v . [c₁₈,ffv] is set
x . (A,B) is Element of the carrier of K
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
x . [A,B] is set
ww is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
w is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
B is Element of the carrier of V
B + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (B + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
A is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
ww . (v,A) is Element of the carrier of K
[v,A] is set
{v,A} is set
{v} is set
{{v,A},{v}} is set
ww . [v,A] is set
x . (B,w) is Element of the carrier of K
[B,w] is set
{B,w} is set
{B} is set
{{B,w},{B}} is set
x . [B,w] is set
w . (v,A) is Element of the carrier of K
w . [v,A] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of (VectQuot (V,(K,V,f,x))) holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
B is set
A is Element of the carrier of f
ww is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of V
w + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
(K,V,f,x) . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
(K,V,f,x) . [ww,A] is set
x . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{w} is set
{{w,A},{w}} is set
x . [w,A] is set
B is set
A is Element of the carrier of f
ww is Element of the carrier of V
ww + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (ww + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
x . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
x . [ww,A] is set
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,V,f,x) . (w,A) is Element of the carrier of K
[w,A] is set
{w,A} is set
{w} is set
{{w,A},{w}} is set
(K,V,f,x) . [w,A] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of (VectQuot (f,(K,V,f,x))) holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
B is set
A is Element of the carrier of V
ww is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
(K,V,f,x) . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
(K,V,f,x) . [A,ww] is set
x . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{{A,w},{A}} is set
x . [A,w] is set
B is set
A is Element of the carrier of V
ww is Element of the carrier of f
ww + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (ww + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
x . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
x . [A,ww] is set
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,f,x) . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{{A,w},{A}} is set
(K,V,f,x) . [A,w] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
the carrier of (K,V,f,x) is non empty set
(K,V,f,x) is non empty Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of (VectQuot (V,(K,V,f,x))) holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
the carrier of (K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
the carrier of (K,V,f,x) is non empty set
(K,V,f,x) is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of (VectQuot (f,(K,V,f,x))) holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
the carrier of (K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] is non empty set
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:]
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
[:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
dom (K,V,f,x) is Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of (VectQuot (f,(K,V,f,x))) -valued Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]
bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
B is set
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
[w,v] is Element of [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]
{w,v} is set
{w} is set
{{w,v},{w}} is set
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v is Element of the carrier of V
v + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
(K,V,f,x) . B is set
(K,V,f,x) . (w,v) is Element of the carrier of K
[w,v] is set
(K,V,f,x) . [w,v] is set
x . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
x . [v,w] is set
(K,V,f,x) . (w,w) is Element of the carrier of K
[w,w] is set
{w,w} is set
{{w,w},{w}} is set
(K,V,f,x) . [w,w] is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (w,v) is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . [w,v] is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . B is set
dom (K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is Relation-like the carrier of (VectQuot (V,(K,V,f,x))) -defined the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) -valued Element of bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):]
bool [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] is non empty set
B is set
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
[w,v] is Element of [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]
{w,v} is set
{w} is set
{{w,v},{w}} is set
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v is Element of the carrier of V
v + (K,V,f,x) is Element of bool the carrier of V
{ (v + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
(K,V,f,x) . B is set
(K,V,f,x) . (w,v) is Element of the carrier of K
[w,v] is set
(K,V,f,x) . [w,v] is set
x . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
x . [v,w] is set
(K,V,f,x) . (v,v) is Element of the carrier of K
[v,v] is set
{v,v} is set
{{v,v},{v}} is set
(K,V,f,x) . [v,v] is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (w,v) is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . [w,v] is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . B is set
dom (K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is Relation-like the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) -defined the carrier of (VectQuot (f,(K,V,f,x))) -valued Element of bool [: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):]
bool [: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
bool the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (f,(K,V,f,x))) holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:]
the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))),(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) holds (K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (b₁,b₂) = 0. K } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
bool the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (V,(K,V,f,x))) holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))),(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))))
bool the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) is non empty set
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) : for b₂ being Element of the carrier of (VectQuot (V,(K,V,f,x))) holds (K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (b₂,b₁) = 0. K } is set
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))),(VectQuot (f,(K,V,f,x))),(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))))
bool the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) is non empty set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) : for b₂ being Element of the carrier of (VectQuot (f,(K,V,f,x))) holds (K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (b₁,b₂) = 0. K } is set
(K,(VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))),(VectQuot (f,(K,V,f,x))),(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) holds (K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (b₂,b₁) = 0. K } is set
A is set
B is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))))
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (B,w) is Element of the carrier of K
[B,w] is set
{B,w} is set
{B} is set
{{B,w},{B}} is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . [B,w] is set
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,f,x) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{{B,v},{B}} is set
(K,V,f,x) . [B,v] is set
A is set
B is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,f,x) . (B,w) is Element of the carrier of K
[B,w] is set
{B,w} is set
{B} is set
{{B,w},{B}} is set
(K,V,f,x) . [B,w] is set
v is Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))))
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{{B,v},{B}} is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . [B,v] is set
A is set
B is Element of the carrier of (VectQuot (f,(K,V,f,x)))
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))))
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . [v,w] is set
(K,V,f,x) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{{v,B},{v}} is set
(K,V,f,x) . [v,B] is set
A is set
B is Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))))
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,f,x) . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
(K,V,f,x) . [v,w] is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{{v,B},{v}} is set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . [v,B] is set
A is set
B is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))))
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . [w,v] is set
(K,V,f,x) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{B} is set
{{B,v},{B}} is set
(K,V,f,x) . [B,v] is set
A is set
B is Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))))
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
v is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,f,x) . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,f,x) . [w,v] is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (B,v) is Element of the carrier of K
[B,v] is set
{B,v} is set
{B} is set
{{B,v},{B}} is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . [B,v] is set
A is set
B is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))))
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{w} is set
{{w,B},{w}} is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . [w,B] is set
v is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,V,f,x) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
(K,V,f,x) . [v,B] is set
A is set
B is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of (VectQuot (V,(K,V,f,x)))
(K,V,f,x) . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{w} is set
{{w,B},{w}} is set
(K,V,f,x) . [w,B] is set
v is Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))))
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (v,B) is Element of the carrier of K
[v,B] is set
{v,B} is set
{v} is set
{{v,B},{v}} is set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . [v,B] is set
K is non empty right_complementable add-associative right_zeroed right-distributive left-distributive distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
ker x is Element of bool the carrier of V
bool the carrier of V is non empty set
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is Element of bool the carrier of V
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds (K,V,f,x,w) . (b₁,b₂) = 0. K } is set
{ b₁ where b₁ is Element of the carrier of V : x . b₁ = 0. K } is set
B is set
A is Element of the carrier of V
x . A is Element of the carrier of K
ww is Element of the carrier of f
(K,V,f,x,w) . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
(K,V,f,x,w) . [A,ww] is set
w . ww is Element of the carrier of K
(x . A) * (w . ww) is Element of the carrier of K
K is non empty right_complementable almost_left_invertible add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
ker x is Element of bool the carrier of V
bool the carrier of V is non empty set
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds (K,V,f,x,w) . (b₁,b₂) = 0. K } is set
{ b₁ where b₁ is Element of the carrier of V : x . b₁ = 0. K } is set
B is set
A is Element of the carrier of V
x . A is Element of the carrier of K
ww is Element of the carrier of f
w . ww is Element of the carrier of K
(x . A) * (w . ww) is Element of the carrier of K
(K,V,f,x,w) . (A,ww) is Element of the carrier of K
[A,ww] is set
{A,ww} is set
{A} is set
{{A,ww},{A}} is set
(K,V,f,x,w) . [A,ww] is set
(0Functional f) . ww is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive left-distributive distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
ker w is Element of bool the carrier of f
bool the carrier of f is non empty set
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is Element of bool the carrier of f
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds (K,V,f,x,w) . (b₂,b₁) = 0. K } is set
{ b₁ where b₁ is Element of the carrier of f : w . b₁ = 0. K } is set
B is set
A is Element of the carrier of f
w . A is Element of the carrier of K
ww is Element of the carrier of V
(K,V,f,x,w) . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
(K,V,f,x,w) . [ww,A] is set
x . ww is Element of the carrier of K
(x . ww) * (w . A) is Element of the carrier of K
K is non empty right_complementable almost_left_invertible add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds (K,V,f,x,w) . (b₂,b₁) = 0. K } is set
ker w is Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : w . b₁ = 0. K } is set
B is set
A is Element of the carrier of f
w . A is Element of the carrier of K
ww is Element of the carrier of V
x . ww is Element of the carrier of K
(x . ww) * (w . A) is Element of the carrier of K
(K,V,f,x,w) . (ww,A) is Element of the carrier of K
[ww,A] is set
{ww,A} is set
{ww} is set
{{ww,A},{ww}} is set
(K,V,f,x,w) . [ww,A] is set
(0Functional V) . ww is Element of the carrier of K
K is non empty right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
Ker x is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(Ker x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(Ker x))) is non empty set
[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:] is non empty set
CQFunctional x is non empty Relation-like the carrier of (VectQuot (V,(Ker x))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (V,(Ker x)))) V21( the carrier of (VectQuot (V,(Ker x))), the carrier of K) additive homogeneous 0-preserving non degenerated Element of bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of K:]
[: the carrier of (VectQuot (V,(Ker x))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of K:] is non empty set
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,(K,V,f,x,w))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))),f) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K:]
[:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w) is non empty Relation-like [: the carrier of (VectQuot (V,(Ker x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(Ker x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(Ker x)),f) (K, VectQuot (V,(Ker x)),f) Element of bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K:]
[:[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty Element of bool the carrier of V
bool the carrier of V is non empty set
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds (K,V,f,x,w) . (b₁,b₂) = 0. K } is set
ker x is non empty Element of bool the carrier of V
the carrier of (K,V,f,(K,V,f,x,w)) is non empty set
v is set
dom (K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w) is Relation-like the carrier of (VectQuot (V,(Ker x))) -defined the carrier of f -valued Element of bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of f:]
bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of f:] is non empty set
A is Element of the carrier of (VectQuot (V,(Ker x)))
B is Element of the carrier of f
[A,B] is Element of [: the carrier of (VectQuot (V,(Ker x))), the carrier of f:]
{A,B} is set
{A} is set
{{A,B},{A}} is set
w is Element of the carrier of V
w + (Ker x) is Element of bool the carrier of V
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in Ker x } is set
(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w) . v is set
(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w) . (A,B) is Element of the carrier of K
[A,B] is set
(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w) . [A,B] is set
(CQFunctional x) . A is Element of the carrier of K
w . B is Element of the carrier of K
((CQFunctional x) . A) * (w . B) is Element of the carrier of K
x . w is Element of the carrier of K
(x . w) * (w . B) is Element of the carrier of K
(K,V,f,x,w) . (w,B) is Element of the carrier of K
[w,B] is set
{w,B} is set
{w} is set
{{w,B},{w}} is set
(K,V,f,x,w) . [w,B] is set
(K,V,f,(K,V,f,x,w)) . (A,B) is set
(K,V,f,(K,V,f,x,w)) . [A,B] is set
(K,V,f,(K,V,f,x,w)) . v is set
dom (K,V,f,(K,V,f,x,w)) is Relation-like the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))) -defined the carrier of f -valued Element of bool [: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:]
bool [: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:] is non empty set
K is non empty right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
0Functional V is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
[#] V is non empty non proper Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] V) --> (0. K) is non empty Relation-like [#] V -defined the carrier of K -valued Function-like V20( [#] V) V21( [#] V, the carrier of K) Element of bool [:([#] V), the carrier of K:]
[:([#] V), the carrier of K:] is non empty set
bool [:([#] V), the carrier of K:] is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like V20( the carrier of V) V21( the carrier of V, the carrier of K) Element of bool [: the carrier of V, the carrier of K:]
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
Ker w is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,(K,V,f,x,w))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):] is non empty set
VectQuot (f,(Ker w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(Ker w))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(Ker w))):] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,(K,V,f,x,w)))) (K,V, VectQuot (f,(K,V,f,(K,V,f,x,w)))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K:]
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K:] is non empty set
CQFunctional w is non empty Relation-like the carrier of (VectQuot (f,(Ker w))) -defined the carrier of K -valued Function-like V20( the carrier of (VectQuot (f,(Ker w)))) V21( the carrier of (VectQuot (f,(Ker w))), the carrier of K) additive homogeneous 0-preserving non degenerated Element of bool [: the carrier of (VectQuot (f,(Ker w))), the carrier of K:]
[: the carrier of (VectQuot (f,(Ker w))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (f,(Ker w))), the carrier of K:] is non empty set
(K,V,(VectQuot (f,(Ker w))),x,(CQFunctional w)) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(Ker w))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(Ker w))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(Ker w))):], the carrier of K) (K,V, VectQuot (f,(Ker w))) (K,V, VectQuot (f,(Ker w))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(Ker w))):], the carrier of K:]
[:[: the carrier of V, the carrier of (VectQuot (f,(Ker w))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(Ker w))):], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty Element of bool the carrier of f
bool the carrier of f is non empty set
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds (K,V,f,x,w) . (b₂,b₁) = 0. K } is set
ker w is non empty Element of bool the carrier of f
the carrier of (K,V,f,(K,V,f,x,w)) is non empty set
v is set
dom (K,V,(VectQuot (f,(Ker w))),x,(CQFunctional w)) is Relation-like the carrier of V -defined the carrier of (VectQuot (f,(Ker w))) -valued Element of bool [: the carrier of V, the carrier of (VectQuot (f,(Ker w))):]
bool [: the carrier of V, the carrier of (VectQuot (f,(Ker w))):] is non empty set
A is Element of the carrier of V
B is Element of the carrier of (VectQuot (f,(Ker w)))
[A,B] is Element of [: the carrier of V, the carrier of (VectQuot (f,(Ker w))):]
{A,B} is set
{A} is set
{{A,B},{A}} is set
w is Element of the carrier of f
w + (Ker w) is Element of bool the carrier of f
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in Ker w } is set
(K,V,(VectQuot (f,(Ker w))),x,(CQFunctional w)) . v is set
(K,V,(VectQuot (f,(Ker w))),x,(CQFunctional w)) . (A,B) is Element of the carrier of K
[A,B] is set
(K,V,(VectQuot (f,(Ker w))),x,(CQFunctional w)) . [A,B] is set
x . A is Element of the carrier of K
(CQFunctional w) . B is Element of the carrier of K
(x . A) * ((CQFunctional w) . B) is Element of the carrier of K
w . w is Element of the carrier of K
(x . A) * (w . w) is Element of the carrier of K
(K,V,f,x,w) . (A,w) is Element of the carrier of K
[A,w] is set
{A,w} is set
{{A,w},{A}} is set
(K,V,f,x,w) . [A,w] is set
(K,V,f,(K,V,f,x,w)) . (A,B) is set
(K,V,f,(K,V,f,x,w)) . [A,B] is set
(K,V,f,(K,V,f,x,w)) . v is set
dom (K,V,f,(K,V,f,x,w)) is Relation-like the carrier of V -defined the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))) -valued Element of bool [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):]
bool [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):] is non empty set
K is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
the carrier of K is non empty non trivial set
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty non trivial set
[: the carrier of f, the carrier of K:] is non empty set
bool [: the carrier of f, the carrier of K:] is non empty set
x is non empty Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
Ker x is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(Ker x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(Ker x))) is non empty set
CQFunctional x is non empty Relation-like the carrier of (VectQuot (V,(Ker x))) -defined the carrier of K -valued Function-like non constant V20( the carrier of (VectQuot (V,(Ker x)))) V21( the carrier of (VectQuot (V,(Ker x))), the carrier of K) additive homogeneous 0-preserving non degenerated Element of bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of K:]
[: the carrier of (VectQuot (V,(Ker x))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of K:] is non empty set
w is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like non constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
(K,V,f,x,w) is non empty non trivial Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like non constant V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
[: the carrier of V, the carrier of f:] is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,(K,V,f,x,w))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))) is non empty set
(K,V,f,(K,V,f,x,w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,(K,V,f,x,w))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):] is non empty set
Ker w is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(Ker w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(Ker w))) is non empty set
[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):]) V21([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,V,f,(K,V,f,x,w)))) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,V,f,(K,V,f,x,w)))) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,V,f,(K,V,f,x,w)))) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,V,f,(K,V,f,x,w)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K:]
[:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,V,f,(K,V,f,x,w)))):], the carrier of K:] is non empty set
CQFunctional w is non empty Relation-like the carrier of (VectQuot (f,(Ker w))) -defined the carrier of K -valued Function-like non constant V20( the carrier of (VectQuot (f,(Ker w)))) V21( the carrier of (VectQuot (f,(Ker w))), the carrier of K) additive homogeneous 0-preserving non degenerated Element of bool [: the carrier of (VectQuot (f,(Ker w))), the carrier of K:]
[: the carrier of (VectQuot (f,(Ker w))), the carrier of K:] is non empty set
bool [: the carrier of (VectQuot (f,(Ker w))), the carrier of K:] is non empty set
(K,(VectQuot (V,(Ker x))),(VectQuot (f,(Ker w))),(CQFunctional x),(CQFunctional w)) is non empty Relation-like [: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):]) V21([: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):], the carrier of K) (K, VectQuot (V,(Ker x)), VectQuot (f,(Ker w))) (K, VectQuot (V,(Ker x)), VectQuot (f,(Ker w))) (K, VectQuot (V,(Ker x)), VectQuot (f,(Ker w))) (K, VectQuot (V,(Ker x)), VectQuot (f,(Ker w))) Element of bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):], the carrier of K:]
[:[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(Ker w))):], the carrier of K:] is non empty set
0Functional (VectQuot (V,(Ker x))) is non empty Relation-like the carrier of (VectQuot (V,(Ker x))) -defined the carrier of K -valued Function-like constant V20( the carrier of (VectQuot (V,(Ker x)))) V21( the carrier of (VectQuot (V,(Ker x))), the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of (VectQuot (V,(Ker x))), the carrier of K:]
[#] (VectQuot (V,(Ker x))) is non empty non proper Element of bool the carrier of (VectQuot (V,(Ker x)))
bool the carrier of (VectQuot (V,(Ker x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
([#] (VectQuot (V,(Ker x)))) --> (0. K) is non empty Relation-like [#] (VectQuot (V,(Ker x))) -defined the carrier of K -valued Function-like V20( [#] (VectQuot (V,(Ker x)))) V21( [#] (VectQuot (V,(Ker x))), the carrier of K) Element of bool [:([#] (VectQuot (V,(Ker x)))), the carrier of K:]
[:([#] (VectQuot (V,(Ker x)))), the carrier of K:] is non empty set
bool [:([#] (VectQuot (V,(Ker x)))), the carrier of K:] is non empty set
0Functional f is non empty Relation-like the carrier of f -defined the carrier of K -valued Function-like constant V20( the carrier of f) V21( the carrier of f, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of f, the carrier of K:]
[#] f is non empty non proper Element of bool the carrier of f
bool the carrier of f is non empty set
([#] f) --> (0. K) is non empty Relation-like [#] f -defined the carrier of K -valued Function-like V20( [#] f) V21( [#] f, the carrier of K) Element of bool [:([#] f), the carrier of K:]
[:([#] f), the carrier of K:] is non empty set
bool [:([#] f), the carrier of K:] is non empty set
[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:] is non empty set
[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:] is non empty set
(K,V,f,(K,V,f,x,w)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))),f) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))),f) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))),f) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K:]
[:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w) is non empty non trivial Relation-like [: the carrier of (VectQuot (V,(Ker x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(Ker x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(Ker x)),f) (K, VectQuot (V,(Ker x)),f) (K, VectQuot (V,(Ker x)),f) (K, VectQuot (V,(Ker x)),f) Element of bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K:]
[:[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):]) V21([: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):], the carrier of K) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))) (K, VectQuot (V,(K,V,f,(K,V,f,x,w))), VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):], the carrier of K:]
(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w)))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,(K,V,f,x,w)))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,(K,V,f,x,w)))),f,(K,V,f,(K,V,f,x,w))))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)) is non empty Relation-like [: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):]) V21([: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):], the carrier of K) (K, VectQuot (V,(Ker x)), VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))) (K, VectQuot (V,(Ker x)), VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))) (K, VectQuot (V,(Ker x)), VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))) (K, VectQuot (V,(Ker x)), VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))) Element of bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):], the carrier of K:]
(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))) is non empty set
[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):] is non empty set
[:[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(Ker x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(Ker x))),f,(K,(VectQuot (V,(Ker x))),f,(CQFunctional x),w)))):], the carrier of K:] is non empty set
K is ZeroStr
V is non empty VectSpStr over K
the carrier of V is non empty set
f is non empty VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_zeroed VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
bool the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of f holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
0. (VectQuot (V,(K,V,f,x))) is V56( VectQuot (V,(K,V,f,x))) Element of the carrier of (VectQuot (V,(K,V,f,x)))
the ZeroF of (VectQuot (V,(K,V,f,x))) is Element of the carrier of (VectQuot (V,(K,V,f,x)))
{(0. (VectQuot (V,(K,V,f,x))))} is Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
A is set
ww is Element of the carrier of (VectQuot (V,(K,V,f,x)))
w is Element of the carrier of V
w + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
v is Element of the carrier of f
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
(K,V,f,x) . (ww,v) is Element of the carrier of K
[ww,v] is set
{ww,v} is set
{ww} is set
{{ww,v},{ww}} is set
(K,V,f,x) . [ww,v] is set
(K,V,f,x) is non empty Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of f holds x . (b₁,b₂) = 0. K } is set
the carrier of (K,V,f,x) is non empty set
zeroCoset (V,(K,V,f,x)) is Element of CosetSet (V,(K,V,f,x))
CosetSet (V,(K,V,f,x)) is non empty Element of bool (bool the carrier of V)
bool (bool the carrier of V) is non empty set
A is set
ww is Element of the carrier of f
(K,V,f,x) . ((0. (VectQuot (V,(K,V,f,x)))),ww) is Element of the carrier of K
[(0. (VectQuot (V,(K,V,f,x)))),ww] is set
{(0. (VectQuot (V,(K,V,f,x)))),ww} is set
{(0. (VectQuot (V,(K,V,f,x))))} is set
{{(0. (VectQuot (V,(K,V,f,x)))),ww},{(0. (VectQuot (V,(K,V,f,x))))}} is set
(K,V,f,x) . [(0. (VectQuot (V,(K,V,f,x)))),ww] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_zeroed VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
bool the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of V holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
0. (VectQuot (f,(K,V,f,x))) is V56( VectQuot (f,(K,V,f,x))) Element of the carrier of (VectQuot (f,(K,V,f,x)))
the ZeroF of (VectQuot (f,(K,V,f,x))) is Element of the carrier of (VectQuot (f,(K,V,f,x)))
{(0. (VectQuot (f,(K,V,f,x))))} is Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
A is set
ww is Element of the carrier of (VectQuot (f,(K,V,f,x)))
w is Element of the carrier of f
w + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (w + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
v is Element of the carrier of V
x . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
x . [v,w] is set
(K,V,f,x) . (v,ww) is Element of the carrier of K
[v,ww] is set
{v,ww} is set
{{v,ww},{v}} is set
(K,V,f,x) . [v,ww] is set
(K,V,f,x) is non empty Element of bool the carrier of f
{ b₁ where b₁ is Element of the carrier of f : for b₂ being Element of the carrier of V holds x . (b₂,b₁) = 0. K } is set
the carrier of (K,V,f,x) is non empty set
zeroCoset (f,(K,V,f,x)) is Element of CosetSet (f,(K,V,f,x))
CosetSet (f,(K,V,f,x)) is non empty Element of bool (bool the carrier of f)
bool (bool the carrier of f) is non empty set
A is set
ww is Element of the carrier of V
(K,V,f,x) . (ww,(0. (VectQuot (f,(K,V,f,x))))) is Element of the carrier of K
[ww,(0. (VectQuot (f,(K,V,f,x))))] is set
{ww,(0. (VectQuot (f,(K,V,f,x))))} is set
{ww} is set
{{ww,(0. (VectQuot (f,(K,V,f,x))))},{ww}} is set
(K,V,f,x) . [ww,(0. (VectQuot (f,(K,V,f,x))))] is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
bool the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of V holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
0. (VectQuot (f,(K,V,f,x))) is V56( VectQuot (f,(K,V,f,x))) Element of the carrier of (VectQuot (f,(K,V,f,x)))
the ZeroF of (VectQuot (f,(K,V,f,x))) is Element of the carrier of (VectQuot (f,(K,V,f,x)))
{(0. (VectQuot (f,(K,V,f,x))))} is Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))),(VectQuot (f,(K,V,f,x))),(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) holds (K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (b₂,b₁) = 0. K } is set
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
bool the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of f holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
0. (VectQuot (V,(K,V,f,x))) is V56( VectQuot (V,(K,V,f,x))) Element of the carrier of (VectQuot (V,(K,V,f,x)))
the ZeroF of (VectQuot (V,(K,V,f,x))) is Element of the carrier of (VectQuot (V,(K,V,f,x)))
{(0. (VectQuot (V,(K,V,f,x))))} is Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:]
the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))),(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) holds (K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (b₁,b₂) = 0. K } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (f,(K,V,f,x))) holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (V,(K,V,f,x))) holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
K is non empty right_complementable Abelian add-associative right_zeroed V130() associative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty set
f is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) (K, VectQuot (V,(K,V,f,x)),f) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:]
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of f:], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:]
the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))):], the carrier of K:] is non empty set
(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
bool the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of f holds (K,V,f,x) . (b₁,b₂) = 0. K } is set
0. (VectQuot (V,(K,V,f,x))) is V56( VectQuot (V,(K,V,f,x))) Element of the carrier of (VectQuot (V,(K,V,f,x)))
the ZeroF of (VectQuot (V,(K,V,f,x))) is Element of the carrier of (VectQuot (V,(K,V,f,x)))
{(0. (VectQuot (V,(K,V,f,x))))} is Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
(K,(VectQuot (V,(K,V,f,x))),(VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))),(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (V,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (V,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (f,(K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)))) holds (K,(VectQuot (V,(K,V,f,x))),f,(K,V,f,x)) . (b₁,b₂) = 0. K } is set
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) (K,V, VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) is non empty set
[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
bool the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of V holds (K,V,f,x) . (b₂,b₁) = 0. K } is set
0. (VectQuot (f,(K,V,f,x))) is V56( VectQuot (f,(K,V,f,x))) Element of the carrier of (VectQuot (f,(K,V,f,x)))
the ZeroF of (VectQuot (f,(K,V,f,x))) is Element of the carrier of (VectQuot (f,(K,V,f,x)))
{(0. (VectQuot (f,(K,V,f,x))))} is Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
(K,(VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))),(VectQuot (f,(K,V,f,x))),(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x))) is non empty Element of bool the carrier of (VectQuot (f,(K,V,f,x)))
{ b₁ where b₁ is Element of the carrier of (VectQuot (f,(K,V,f,x))) : for b₂ being Element of the carrier of (VectQuot (V,(K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)))) holds (K,V,(VectQuot (f,(K,V,f,x))),(K,V,f,x)) . (b₂,b₁) = 0. K } is set
K is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty non trivial set
f is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of f is non empty non trivial set
[: the carrier of V, the carrier of f:] is non empty set
the carrier of K is non empty non trivial set
[:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of f:], the carrier of K:] is non empty set
x is non empty Relation-like [: the carrier of V, the carrier of f:] -defined the carrier of K -valued Function-like non constant V20([: the carrier of V, the carrier of f:]) V21([: the carrier of V, the carrier of f:], the carrier of K) (K,V,f) (K,V,f) (K,V,f) (K,V,f) Element of bool [:[: the carrier of V, the carrier of f:], the carrier of K:]
(K,V,f,x) is non empty Relation-like [: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] -defined the carrier of K -valued Function-like V20([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):]) V21([: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) (K, VectQuot (V,(K,V,f,x)), VectQuot (f,(K,V,f,x))) Element of bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:]
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of V
VectQuot (V,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (V,(K,V,f,x))) is non empty set
(K,V,f,x) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of f
VectQuot (f,(K,V,f,x)) is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of (VectQuot (f,(K,V,f,x))) is non empty set
[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):] is non empty set
[:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
bool [:[: the carrier of (VectQuot (V,(K,V,f,x))), the carrier of (VectQuot (f,(K,V,f,x))):], the carrier of K:] is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
w is Element of the carrier of V
v is Element of the carrier of f
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
v + (K,V,f,x) is Element of bool the carrier of f
bool the carrier of f is non empty set
{ (v + b₁) where b₁ is Element of the carrier of f : b₁ in (K,V,f,x) } is set
w + (K,V,f,x) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (w + b₁) where b₁ is Element of the carrier of V : b₁ in (K,V,f,x) } is set
A is Element of the carrier of (VectQuot (V,(K,V,f,x)))
B is Element of the carrier of (VectQuot (f,(K,V,f,x)))
(K,V,f,x) . (A,B) is Element of the carrier of K
[A,B] is set
{A,B} is set
{A} is set
{{A,B},{A}} is set
(K,V,f,x) . [A,B] is set
K is 1-sorted
V is VectSpStr over K
the carrier of V is set
[: the carrier of V, the carrier of V:] is set
the carrier of K is set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
K is ZeroStr
V is VectSpStr over K
the carrier of V is set
[: the carrier of V, the carrier of V:] is set
the carrier of K is set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
K is non empty ZeroStr
V is non empty VectSpStr over K
(K,V,V) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of V:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
f is Element of the carrier of V
x is Element of the carrier of V
(K,V,V) . (f,x) is set
[f,x] is set
{f,x} is set
{f} is set
{{f,x},{f}} is set
(K,V,V) . [f,x] is set
(K,V,V) . (x,f) is set
[x,f] is set
{x,f} is set
{x} is set
{{x,f},{x}} is set
(K,V,V) . [x,f] is set
(K,V,V) . (f,x) is Element of the carrier of K
(K,V,V) . (x,f) is Element of the carrier of K
f is Element of the carrier of V
(K,V,V) . (f,f) is set
[f,f] is set
{f,f} is set
{f} is set
{{f,f},{f}} is set
(K,V,V) . [f,f] is set
(K,V,V) . (f,f) is Element of the carrier of K
K is non empty ZeroStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
(K,V,V) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of V:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of V:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
(K,V,V) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V,V) (K,V,V) (K,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of V:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V,V) (K,V,V) (K,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of V:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
K is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital doubleLoopStr
V is non empty non trivial right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital VectSpStr over K
the carrier of V is non empty non trivial set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty non trivial set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
[: the carrier of V, the carrier of K:] is non empty set
bool [: the carrier of V, the carrier of K:] is non empty set
the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:] is non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]
(K,V,V, the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:], the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:]) is non empty non trivial Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like non constant V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V,V) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is non empty non trivial Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like non constant V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V,V) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of V
x . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
x . [w,v] is set
the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:] . w is Element of the carrier of K
the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:] . v is Element of the carrier of K
( the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:] . w) * ( the non empty non trivial Relation-like the carrier of V -defined the carrier of K -valued Function-like non constant V20( the carrier of V) V21( the carrier of V, the carrier of K) additive homogeneous 0-preserving Element of bool [: the carrier of V, the carrier of K:] . v) is Element of the carrier of K
x . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
x . [v,w] is set
K is non empty right_complementable add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
(K,V,V) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
[: the carrier of V, the carrier of V:] --> (0. K) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of V
(K,V,V,f,x) . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,V,f,x) . [w,v] is set
(K,V,V,f,x) . (v,w) is set
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
(K,V,V,f,x) . [v,w] is set
(K,V,V,f,x) . (w,v) is Element of the carrier of K
f . (w,v) is Element of the carrier of K
f . [w,v] is set
x . (w,v) is Element of the carrier of K
x . [w,v] is set
(f . (w,v)) + (x . (w,v)) is Element of the carrier of K
f . (v,w) is Element of the carrier of K
f . [v,w] is set
(f . (v,w)) + (x . (w,v)) is Element of the carrier of K
x . (v,w) is Element of the carrier of K
x . [v,w] is set
(f . (v,w)) + (x . (v,w)) is Element of the carrier of K
(K,V,V,f,x) . (v,w) is Element of the carrier of K
K is non empty doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is Element of the carrier of K
(K,V,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
w is Element of the carrier of V
v is Element of the carrier of V
(K,V,V,f,x) . (w,v) is set
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
(K,V,V,f,x) . [w,v] is set
(K,V,V,f,x) . (v,w) is set
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
(K,V,V,f,x) . [v,w] is set
(K,V,V,f,x) . (w,v) is Element of the carrier of K
f . (w,v) is Element of the carrier of K
f . [w,v] is set
x * (f . (w,v)) is Element of the carrier of K
f . (v,w) is Element of the carrier of K
f . [v,w] is set
x * (f . (v,w)) is Element of the carrier of K
(K,V,V,f,x) . (v,w) is Element of the carrier of K
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is Element of the carrier of V
w is Element of the carrier of V
(K,V,V,f) . (x,w) is set
[x,w] is set
{x,w} is set
{x} is set
{{x,w},{x}} is set
(K,V,V,f) . [x,w] is set
(K,V,V,f) . (w,x) is set
[w,x] is set
{w,x} is set
{w} is set
{{w,x},{w}} is set
(K,V,V,f) . [w,x] is set
(K,V,V,f) . (x,w) is Element of the carrier of K
f . (x,w) is Element of the carrier of K
f . [x,w] is set
- (f . (x,w)) is Element of the carrier of K
f . (w,x) is Element of the carrier of K
f . [w,x] is set
- (f . (w,x)) is Element of the carrier of K
(K,V,V,f) . (w,x) is Element of the carrier of K
K is non empty addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f,(K,V,V,x)) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
K is non empty right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
w is Element of the carrier of V
(K,V,V,f,x) . (w,w) is set
[w,w] is set
{w,w} is set
{w} is set
{{w,w},{w}} is set
(K,V,V,f,x) . [w,w] is set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(K,V,V,f,x) . (w,w) is Element of the carrier of K
f . (w,w) is Element of the carrier of K
f . [w,w] is set
x . (w,w) is Element of the carrier of K
x . [w,w] is set
(f . (w,w)) + (x . (w,w)) is Element of the carrier of K
(0. K) + (x . (w,w)) is Element of the carrier of K
(0. K) + (0. K) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is Element of the carrier of K
(K,V,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
w is Element of the carrier of V
(K,V,V,f,x) . (w,w) is set
[w,w] is set
{w,w} is set
{w} is set
{{w,w},{w}} is set
(K,V,V,f,x) . [w,w] is set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(K,V,V,f,x) . (w,w) is Element of the carrier of K
f . (w,w) is Element of the carrier of K
f . [w,w] is set
x * (f . (w,w)) is Element of the carrier of K
x * (0. K) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is Element of the carrier of V
(K,V,V,f) . (x,x) is set
[x,x] is set
{x,x} is set
{x} is set
{{x,x},{x}} is set
(K,V,V,f) . [x,x] is set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
(K,V,V,f) . (x,x) is Element of the carrier of K
f . (x,x) is Element of the carrier of K
f . [x,x] is set
- (f . (x,x)) is Element of the carrier of K
- (0. K) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed addLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,x) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f,(K,V,V,x)) is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
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 K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V,V) (K,V,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₁,b₂) = 0. K } is set
(K,V,V,f) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₂,b₁) = 0. K } is set
x is set
w is Element of the carrier of V
v is Element of the carrier of V
f . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
f . [v,w] is set
f . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
f . [w,v] is set
x is set
w is Element of the carrier of V
v is Element of the carrier of V
f . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
f . [w,v] is set
f . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
f . [v,w] is set
K is non empty right_complementable add-associative right_zeroed addLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
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 K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is Element of the carrier of V
w is Element of the carrier of V
f . (x,w) is Element of the carrier of K
[x,w] is set
{x,w} is set
{x} is set
{{x,w},{x}} is set
f . [x,w] is set
f . (w,x) is Element of the carrier of K
[w,x] is set
{w,x} is set
{w} is set
{{w,x},{w}} is set
f . [w,x] is set
- (f . (w,x)) is Element of the carrier of K
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
x + w is Element of the carrier of V
f . ((x + w),(x + w)) is Element of the carrier of K
[(x + w),(x + w)] is set
{(x + w),(x + w)} is set
{(x + w)} is set
{{(x + w),(x + w)},{(x + w)}} is set
f . [(x + w),(x + w)] is set
f . (x,x) is Element of the carrier of K
[x,x] is set
{x,x} is set
{{x,x},{x}} is set
f . [x,x] is set
(f . (x,x)) + (f . (x,w)) is Element of the carrier of K
f . (w,w) is Element of the carrier of K
[w,w] is set
{w,w} is set
{{w,w},{w}} is set
f . [w,w] is set
(f . (w,x)) + (f . (w,w)) is Element of the carrier of K
((f . (x,x)) + (f . (x,w))) + ((f . (w,x)) + (f . (w,w))) is Element of the carrier of K
(0. K) + (f . (x,w)) is Element of the carrier of K
((0. K) + (f . (x,w))) + ((f . (w,x)) + (f . (w,w))) is Element of the carrier of K
(f . (w,x)) + (0. K) is Element of the carrier of K
((0. K) + (f . (x,w))) + ((f . (w,x)) + (0. K)) is Element of the carrier of K
((0. K) + (f . (x,w))) + (f . (w,x)) is Element of the carrier of K
(f . (x,w)) + (f . (w,x)) is Element of the carrier of K
K is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed V130() associative commutative right-distributive left-distributive right_unital well-unital distributive left_unital Fanoian doubleLoopStr
V is non empty VectSpStr over K
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
the carrier of K is non empty non trivial set
[:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
x is Element of the carrier of V
w is Element of the carrier of V
f . (x,w) is Element of the carrier of K
[x,w] is set
{x,w} is set
{x} is set
{{x,w},{x}} is set
f . [x,w] is set
f . (w,x) is Element of the carrier of K
[w,x] is set
{w,x} is set
{w} is set
{{w,x},{w}} is set
f . [w,x] is set
- (f . (w,x)) is Element of the carrier of K
x is Element of the carrier of V
f . (x,x) is set
[x,x] is set
{x,x} is set
{x} is set
{{x,x},{x}} is set
f . [x,x] is set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
f . (x,x) is Element of the carrier of K
- (f . (x,x)) is Element of the carrier of K
(f . (x,x)) + (f . (x,x)) is Element of the carrier of K
K is non empty right_complementable add-associative right_zeroed right-distributive doubleLoopStr
the carrier of K is non empty set
V is non empty VectSpStr over K
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 K:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of K:] is non empty set
f is non empty Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of K -valued Function-like V20([: the carrier of V, the carrier of V:]) V21([: the carrier of V, the carrier of V:], the carrier of K) (K,V,V) (K,V,V) (K,V,V) (K,V,V) (K,V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of K:]
(K,V,V,f) is Element of bool the carrier of V
bool the carrier of V is non empty set
0. K is V56(K) Element of the carrier of K
the ZeroF of K is Element of the carrier of K
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₁,b₂) = 0. K } is set
(K,V,V,f) is Element of bool the carrier of V
{ b₁ where b₁ is Element of the carrier of V : for b₂ being Element of the carrier of V holds f . (b₂,b₁) = 0. K } is set
x is set
w is Element of the carrier of V
v is Element of the carrier of V
f . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
f . [v,w] is set
f . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
f . [w,v] is set
- (f . (w,v)) is Element of the carrier of K
- (0. K) is Element of the carrier of K
x is set
w is Element of the carrier of V
v is Element of the carrier of V
f . (w,v) is Element of the carrier of K
[w,v] is set
{w,v} is set
{w} is set
{{w,v},{w}} is set
f . [w,v] is set
f . (v,w) is Element of the carrier of K
[v,w] is set
{v,w} is set
{v} is set
{{v,w},{v}} is set
f . [v,w] is set
- (f . (v,w)) is Element of the carrier of K
- (0. K) is Element of the carrier of K