K140() is Element of bool K136()
K136() is set
bool K136() is non empty set
K135() is set
bool K135() is non empty set
bool K140() is non empty set
{} is empty set
1 is non empty set
0 is empty Element of K140()
{0} is non empty set
X is non empty set
o is Element of X
[:X,X:] is non empty set
[:[:X,X:],X:] is non empty set
bool [:[:X,X:],X:] is non empty set
md is V1() V4([:X,X:]) V5(X) Function-like V18([:X,X:],X) Element of bool [:[:X,X:],X:]
b is set
a is set
bool [:X,X:] is non empty set
a is V1() V4(X) V5(X) Element of bool [:X,X:]
x is V1() V4(X) V5(X) Element of bool [:X,X:]
y is set
z is set
0F is Element of X
p is Element of X
[0F,p] is Element of [:X,X:]
{0F,p} is non empty set
{0F} is non empty set
{{0F,p},{0F}} is non empty set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
[: the carrier of F,X:] is non empty set
[:[: the carrier of F,X:],X:] is non empty set
bool [:[: the carrier of F,X:],X:] is non empty set
S is V1() V4([: the carrier of F,X:]) V5(X) Function-like V18([: the carrier of F,X:],X) Element of bool [:[: the carrier of F,X:],X:]
b is V1() V4(X) V5(X) Element of bool [:X,X:]
SymStr(# X,md,o,S,b #) is non empty strict SymStr over F
the carrier of SymStr(# X,md,o,S,b #) is non empty set
0. SymStr(# X,md,o,S,b #) is V53( SymStr(# X,md,o,S,b #)) Element of the carrier of SymStr(# X,md,o,S,b #)
x is Element of the carrier of SymStr(# X,md,o,S,b #)
x + (0. SymStr(# X,md,o,S,b #)) is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) is V1() V4([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):]) V5( the carrier of SymStr(# X,md,o,S,b #)) Function-like V18([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #)) Element of bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):]
[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):] is non empty set
[:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
the addF of SymStr(# X,md,o,S,b #) . (x,(0. SymStr(# X,md,o,S,b #))) is Element of the carrier of SymStr(# X,md,o,S,b #)
[x,(0. SymStr(# X,md,o,S,b #))] is set
{x,(0. SymStr(# X,md,o,S,b #))} is non empty set
{x} is non empty set
{{x,(0. SymStr(# X,md,o,S,b #))},{x}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [x,(0. SymStr(# X,md,o,S,b #))] is set
md . (x,(0. SymStr(# X,md,o,S,b #))) is set
md . [x,(0. SymStr(# X,md,o,S,b #))] is set
x is Element of the carrier of SymStr(# X,md,o,S,b #)
- x is Element of the carrier of SymStr(# X,md,o,S,b #)
x + (- x) is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) is V1() V4([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):]) V5( the carrier of SymStr(# X,md,o,S,b #)) Function-like V18([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #)) Element of bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):]
[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):] is non empty set
[:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
the addF of SymStr(# X,md,o,S,b #) . (x,(- x)) is Element of the carrier of SymStr(# X,md,o,S,b #)
[x,(- x)] is set
{x,(- x)} is non empty set
{x} is non empty set
{{x,(- x)},{x}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [x,(- x)] is set
x is Element of the carrier of SymStr(# X,md,o,S,b #)
y is Element of the carrier of SymStr(# X,md,o,S,b #)
x + y is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) is V1() V4([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):]) V5( the carrier of SymStr(# X,md,o,S,b #)) Function-like V18([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #)) Element of bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):]
[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):] is non empty set
[:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
the addF of SymStr(# X,md,o,S,b #) . (x,y) is Element of the carrier of SymStr(# X,md,o,S,b #)
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [x,y] is set
z is Element of the carrier of SymStr(# X,md,o,S,b #)
(x + y) + z is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) . ((x + y),z) is Element of the carrier of SymStr(# X,md,o,S,b #)
[(x + y),z] is set
{(x + y),z} is non empty set
{(x + y)} is non empty set
{{(x + y),z},{(x + y)}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [(x + y),z] is set
y + z is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) . (y,z) is Element of the carrier of SymStr(# X,md,o,S,b #)
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [y,z] is set
x + (y + z) is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) . (x,(y + z)) is Element of the carrier of SymStr(# X,md,o,S,b #)
[x,(y + z)] is set
{x,(y + z)} is non empty set
{{x,(y + z)},{x}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [x,(y + z)] is set
0F is Element of X
p is Element of X
r is Element of X
md . (p,r) is Element of X
[p,r] is set
{p,r} is non empty set
{p} is non empty set
{{p,r},{p}} is non empty set
md . [p,r] is set
md . (0F,(md . (p,r))) is Element of X
[0F,(md . (p,r))] is set
{0F,(md . (p,r))} is non empty set
{0F} is non empty set
{{0F,(md . (p,r))},{0F}} is non empty set
md . [0F,(md . (p,r))] is set
x is Element of the carrier of SymStr(# X,md,o,S,b #)
y is Element of the carrier of SymStr(# X,md,o,S,b #)
x + y is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) is V1() V4([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):]) V5( the carrier of SymStr(# X,md,o,S,b #)) Function-like V18([: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #)) Element of bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):]
[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):] is non empty set
[:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
bool [:[: the carrier of SymStr(# X,md,o,S,b #), the carrier of SymStr(# X,md,o,S,b #):], the carrier of SymStr(# X,md,o,S,b #):] is non empty set
the addF of SymStr(# X,md,o,S,b #) . (x,y) is Element of the carrier of SymStr(# X,md,o,S,b #)
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [x,y] is set
y + x is Element of the carrier of SymStr(# X,md,o,S,b #)
the addF of SymStr(# X,md,o,S,b #) . (y,x) is Element of the carrier of SymStr(# X,md,o,S,b #)
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
the addF of SymStr(# X,md,o,S,b #) . [y,x] is set
md . (x,y) is set
md . [x,y] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
[: the carrier of F,X:] is non empty set
[:[: the carrier of F,X:],X:] is non empty set
bool [:[: the carrier of F,X:],X:] is non empty set
S is V1() V4([: the carrier of F,X:]) V5(X) Function-like V18([: the carrier of F,X:],X) Element of bool [:[: the carrier of F,X:],X:]
a is non empty right_complementable Abelian add-associative right_zeroed SymStr over F
b is V1() V4(X) V5(X) Element of bool [:X,X:]
SymStr(# X,md,o,S,b #) is non empty strict SymStr over F
the carrier of a is non empty set
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
x is Element of the carrier of F
y is Element of the carrier of F
x + y is Element of the carrier of F
the addF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the addF of F . (x,y) is Element of the carrier of F
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of F . [x,y] is set
x * y is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
the multF of F . (x,y) is Element of the carrier of F
the multF of F . [x,y] is set
z is Element of the carrier of a
0F is Element of the carrier of a
z + 0F is Element of the carrier of a
the addF of a is V1() V4([: the carrier of a, the carrier of a:]) V5( the carrier of a) Function-like V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (z,0F) is Element of the carrier of a
[z,0F] is set
{z,0F} is non empty set
{z} is non empty set
{{z,0F},{z}} is non empty set
the addF of a . [z,0F] is set
x * (z + 0F) is Element of the carrier of a
x * z is Element of the carrier of a
x * 0F is Element of the carrier of a
(x * z) + (x * 0F) is Element of the carrier of a
the addF of a . ((x * z),(x * 0F)) is Element of the carrier of a
[(x * z),(x * 0F)] is set
{(x * z),(x * 0F)} is non empty set
{(x * z)} is non empty set
{{(x * z),(x * 0F)},{(x * z)}} is non empty set
the addF of a . [(x * z),(x * 0F)] is set
(x + y) * z is Element of the carrier of a
y * z is Element of the carrier of a
(x * z) + (y * z) is Element of the carrier of a
the addF of a . ((x * z),(y * z)) is Element of the carrier of a
[(x * z),(y * z)] is set
{(x * z),(y * z)} is non empty set
{{(x * z),(y * z)},{(x * z)}} is non empty set
the addF of a . [(x * z),(y * z)] is set
(x * y) * z is Element of the carrier of a
x * (y * z) is Element of the carrier of a
(1_ F) * z is Element of the carrier of a
S . ((x * y),z) is set
[(x * y),z] is set
{(x * y),z} is non empty set
{(x * y)} is non empty set
{{(x * y),z},{(x * y)}} is non empty set
S . [(x * y),z] is set
r is Element of the carrier of a
v is Element of the carrier of a
(x * y) * v is Element of the carrier of a
v is Element of the carrier of a
S . (y,v) is set
[y,v] is set
{y,v} is non empty set
{y} is non empty set
{{y,v},{y}} is non empty set
S . [y,v] is set
v is Element of the carrier of a
y * v is Element of the carrier of a
x * (y * v) is Element of the carrier of a
S . (x,o) is Element of X
[x,o] is set
{x,o} is non empty set
{{x,o},{x}} is non empty set
S . [x,o] is set
0. a is V53(a) Element of the carrier of a
p is Element of the carrier of a
r is Element of the carrier of a
v is Element of X
v is Element of X
md . (v,v) is Element of X
[v,v] is set
{v,v} is non empty set
{v} is non empty set
{{v,v},{v}} is non empty set
md . [v,v] is set
v is Element of the carrier of a
v is Element of the carrier of a
v + v is Element of the carrier of a
the addF of a . (v,v) is Element of the carrier of a
[v,v] is set
{v,v} is non empty set
{v} is non empty set
{{v,v},{v}} is non empty set
the addF of a . [v,v] is set
x * (v + v) is Element of the carrier of a
S . (x,o) is Element of X
[x,o] is set
{x,o} is non empty set
{{x,o},{x}} is non empty set
S . [x,o] is set
v is Element of the carrier of a
S . (x,v) is set
[x,v] is set
{x,v} is non empty set
{{x,v},{x}} is non empty set
S . [x,v] is set
v is Element of the carrier of a
S . (x,v) is set
[x,v] is set
{x,v} is non empty set
{{x,v},{x}} is non empty set
S . [x,v] is set
w is Element of the carrier of a
x * w is Element of the carrier of a
v is Element of the carrier of a
x * v is Element of the carrier of a
S . ((x + y),z) is set
[(x + y),z] is set
{(x + y),z} is non empty set
{(x + y)} is non empty set
{{(x + y),z},{(x + y)}} is non empty set
S . [(x + y),z] is set
r is Element of the carrier of a
v is Element of the carrier of a
(x + y) * v is Element of the carrier of a
v is Element of the carrier of a
S . (x,v) is set
[x,v] is set
{x,v} is non empty set
{{x,v},{x}} is non empty set
S . [x,v] is set
v is Element of the carrier of a
x * v is Element of the carrier of a
v is Element of the carrier of a
S . (y,v) is set
[y,v] is set
{y,v} is non empty set
{y} is non empty set
{{y,v},{y}} is non empty set
S . [y,v] is set
0. a is V53(a) Element of the carrier of a
v is Element of the carrier of a
y * v is Element of the carrier of a
S . ((1_ F),z) is set
[(1_ F),z] is set
{(1_ F),z} is non empty set
{(1_ F)} is non empty set
{{(1_ F),z},{(1_ F)}} is non empty set
S . [(1_ F),z] is set
r is Element of the carrier of a
S . ((1_ F),r) is set
[(1_ F),r] is set
{(1_ F),r} is non empty set
{{(1_ F),r},{(1_ F)}} is non empty set
S . [(1_ F),r] is set
S is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of S is non empty non trivial set
[: the carrier of S,X:] is non empty set
[:[: the carrier of S,X:],X:] is non empty set
bool [:[: the carrier of S,X:],X:] is non empty set
a is V1() V4(X) V5(X) Element of bool [:X,X:]
x is non empty right_complementable Abelian add-associative right_zeroed SymStr over S
b is V1() V4([: the carrier of S,X:]) V5(X) Function-like V18([: the carrier of S,X:],X) Element of bool [:[: the carrier of S,X:],X:]
SymStr(# X,md,o,b,a #) is non empty strict SymStr over S
0. x is V53(x) Element of the carrier of x
the carrier of x is non empty set
y is Element of the carrier of x
z is Element of the carrier of x
0F is Element of the carrier of x
p is Element of the carrier of x
y is Element of the carrier of x
z is Element of the carrier of x
[y,z] is Element of [: the carrier of x, the carrier of x:]
[: the carrier of x, the carrier of x:] is non empty set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
0F is Element of X
p is Element of X
[0F,p] is Element of [:X,X:]
{0F,p} is non empty set
{0F} is non empty set
{{0F,p},{0F}} is non empty set
y is Element of the carrier of x
z is Element of the carrier of x
0F is Element of the carrier of x
p is Element of the carrier of x
[y,z] is Element of [: the carrier of x, the carrier of x:]
[: the carrier of x, the carrier of x:] is non empty set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
[0F,p] is Element of [: the carrier of x, the carrier of x:]
{0F,p} is non empty set
{0F} is non empty set
{{0F,p},{0F}} is non empty set
[y,z] is Element of [: the carrier of x, the carrier of x:]
[: the carrier of x, the carrier of x:] is non empty set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
0F is Element of X
p is Element of X
[0F,p] is Element of [:X,X:]
{0F,p} is non empty set
{0F} is non empty set
{{0F,p},{0F}} is non empty set
y is Element of the carrier of x
z is Element of the carrier of x
0F is Element of the carrier of S
0F * y is Element of the carrier of x
z is Element of the carrier of x
y is Element of the carrier of x
0F is Element of the carrier of x
z + 0F is Element of the carrier of x
the addF of x is V1() V4([: the carrier of x, the carrier of x:]) V5( the carrier of x) Function-like V18([: the carrier of x, the carrier of x:], the carrier of x) Element of bool [:[: the carrier of x, the carrier of x:], the carrier of x:]
[: the carrier of x, the carrier of x:] is non empty set
[:[: the carrier of x, the carrier of x:], the carrier of x:] is non empty set
bool [:[: the carrier of x, the carrier of x:], the carrier of x:] is non empty set
the addF of x . (z,0F) is Element of the carrier of x
[z,0F] is set
{z,0F} is non empty set
{z} is non empty set
{{z,0F},{z}} is non empty set
the addF of x . [z,0F] is set
z is Element of the carrier of x
y is Element of the carrier of x
0F is Element of the carrier of x
y is Element of the carrier of x
z is Element of the carrier of x
0F is Element of the carrier of x
z - 0F is Element of the carrier of x
- 0F is Element of the carrier of x
z + (- 0F) is Element of the carrier of x
the addF of x is V1() V4([: the carrier of x, the carrier of x:]) V5( the carrier of x) Function-like V18([: the carrier of x, the carrier of x:], the carrier of x) Element of bool [:[: the carrier of x, the carrier of x:], the carrier of x:]
[: the carrier of x, the carrier of x:] is non empty set
[:[: the carrier of x, the carrier of x:], the carrier of x:] is non empty set
bool [:[: the carrier of x, the carrier of x:], the carrier of x:] is non empty set
the addF of x . (z,(- 0F)) is Element of the carrier of x
[z,(- 0F)] is set
{z,(- 0F)} is non empty set
{z} is non empty set
{{z,(- 0F)},{z}} is non empty set
the addF of x . [z,(- 0F)] is set
0F - y is Element of the carrier of x
- y is Element of the carrier of x
0F + (- y) is Element of the carrier of x
the addF of x . (0F,(- y)) is Element of the carrier of x
[0F,(- y)] is set
{0F,(- y)} is non empty set
{0F} is non empty set
{{0F,(- y)},{0F}} is non empty set
the addF of x . [0F,(- y)] is set
y - z is Element of the carrier of x
- z is Element of the carrier of x
y + (- z) is Element of the carrier of x
the addF of x . (y,(- z)) is Element of the carrier of x
[y,(- z)] is set
{y,(- z)} is non empty set
{y} is non empty set
{{y,(- z)},{y}} is non empty set
the addF of x . [y,(- z)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
[: the carrier of F,X:] is non empty set
[:[: the carrier of F,X:],X:] is non empty set
bool [:[: the carrier of F,X:],X:] is non empty set
[: the carrier of F,X:] --> o is V1() V4([: the carrier of F,X:]) V5(X) Function-like V18([: the carrier of F,X:],X) Element of bool [:[: the carrier of F,X:],X:]
b is V1() V4(X) V5(X) Element of bool [:X,X:]
S is V1() V4([: the carrier of F,X:]) V5(X) Function-like V18([: the carrier of F,X:],X) Element of bool [:[: the carrier of F,X:],X:]
SymStr(# X,md,o,S,b #) is non empty strict SymStr over F
a is non empty right_complementable Abelian add-associative right_zeroed SymStr over F
the carrier of a is non empty set
0. a is V53(a) Element of the carrier of a
x is Element of the carrier of a
y is Element of the carrier of a
z is Element of the carrier of a
0F is Element of the carrier of a
p is Element of the carrier of a
r is Element of the carrier of a
v is Element of the carrier of F
v * p is Element of the carrier of a
v is Element of the carrier of a
v is Element of the carrier of a
v is Element of the carrier of a
v + v is Element of the carrier of a
the addF of a is V1() V4([: the carrier of a, the carrier of a:]) V5( the carrier of a) Function-like V18([: the carrier of a, the carrier of a:], the carrier of a) Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . (v,v) is Element of the carrier of a
[v,v] is set
{v,v} is non empty set
{v} is non empty set
{{v,v},{v}} is non empty set
the addF of a . [v,v] is set
v is Element of the carrier of a
v is Element of the carrier of a
v is Element of the carrier of a
w is Element of the carrier of a
c22 is Element of the carrier of a
c23 is Element of the carrier of a
c22 - c23 is Element of the carrier of a
- c23 is Element of the carrier of a
c22 + (- c23) is Element of the carrier of a
the addF of a . (c22,(- c23)) is Element of the carrier of a
[c22,(- c23)] is set
{c22,(- c23)} is non empty set
{c22} is non empty set
{{c22,(- c23)},{c22}} is non empty set
the addF of a . [c22,(- c23)] is set
c23 - w is Element of the carrier of a
- w is Element of the carrier of a
c23 + (- w) is Element of the carrier of a
the addF of a . (c23,(- w)) is Element of the carrier of a
[c23,(- w)] is set
{c23,(- w)} is non empty set
{c23} is non empty set
{{c23,(- w)},{c23}} is non empty set
the addF of a . [c23,(- w)] is set
w - c22 is Element of the carrier of a
- c22 is Element of the carrier of a
w + (- c22) is Element of the carrier of a
the addF of a . (w,(- c22)) is Element of the carrier of a
[w,(- c22)] is set
{w,(- c22)} is non empty set
{w} is non empty set
{{w,(- c22)},{w}} is non empty set
the addF of a . [w,(- c22)] is set
x is Element of the carrier of F
y is Element of X
[x,y] is Element of [: the carrier of F,X:]
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
S . [x,y] is Element of X
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
0. S is V53(S) Element of the carrier of S
b is Element of the carrier of S
0. F is V53(F) Element of the carrier of F
the carrier of F is non empty non trivial set
y is Element of the carrier of F
y * b is Element of the carrier of S
(0. S) - (y * b) is Element of the carrier of S
- (y * b) is Element of the carrier of S
(0. S) + (- (y * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . ((0. S),(- (y * b))) is Element of the carrier of S
[(0. S),(- (y * b))] is set
{(0. S),(- (y * b))} is non empty set
{(0. S)} is non empty set
{{(0. S),(- (y * b))},{(0. S)}} is non empty set
the addF of S . [(0. S),(- (y * b))] is set
(0. F) * ((0. S) - (y * b)) is Element of the carrier of S
(0. F) * b is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
0. S is V53(S) Element of the carrier of S
- a is Element of the carrier of S
- (- a) is Element of the carrier of S
(0. S) - (- a) is Element of the carrier of S
(0. S) + (- (- a)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . ((0. S),(- (- a))) is Element of the carrier of S
[(0. S),(- (- a))] is set
{(0. S),(- (- a))} is non empty set
{(0. S)} is non empty set
{{(0. S),(- (- a))},{(0. S)}} is non empty set
the addF of S . [(0. S),(- (- a))] is set
(- a) - b is Element of the carrier of S
- b is Element of the carrier of S
(- a) + (- b) is Element of the carrier of S
the addF of S . ((- a),(- b)) is Element of the carrier of S
[(- a),(- b)] is set
{(- a),(- b)} is non empty set
{(- a)} is non empty set
{{(- a),(- b)},{(- a)}} is non empty set
the addF of S . [(- a),(- b)] is set
b - (0. S) is Element of the carrier of S
- (0. S) is Element of the carrier of S
b + (- (0. S)) is Element of the carrier of S
the addF of S . (b,(- (0. S))) is Element of the carrier of S
[b,(- (0. S))] is set
{b,(- (0. S))} is non empty set
{b} is non empty set
{{b,(- (0. S))},{b}} is non empty set
the addF of S . [b,(- (0. S))] is set
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
- (1_ F) is Element of the carrier of F
(- (1_ F)) * (- a) is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
x + b is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,b) is Element of the carrier of S
[x,b] is set
{x,b} is non empty set
{x} is non empty set
{{x,b},{x}} is non empty set
the addF of S . [x,b] is set
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
- (1_ F) is Element of the carrier of F
(- (1_ F)) * x is Element of the carrier of S
- x is Element of the carrier of S
(- x) + (x + b) is Element of the carrier of S
the addF of S . ((- x),(x + b)) is Element of the carrier of S
[(- x),(x + b)] is set
{(- x),(x + b)} is non empty set
{(- x)} is non empty set
{{(- x),(x + b)},{(- x)}} is non empty set
the addF of S . [(- x),(x + b)] is set
x + (- x) is Element of the carrier of S
the addF of S . (x,(- x)) is Element of the carrier of S
[x,(- x)] is set
{x,(- x)} is non empty set
{{x,(- x)},{x}} is non empty set
the addF of S . [x,(- x)] is set
(x + (- x)) + b is Element of the carrier of S
the addF of S . ((x + (- x)),b) is Element of the carrier of S
[(x + (- x)),b] is set
{(x + (- x)),b} is non empty set
{(x + (- x))} is non empty set
{{(x + (- x)),b},{(x + (- x))}} is non empty set
the addF of S . [(x + (- x)),b] is set
0. S is V53(S) Element of the carrier of S
(0. S) + b is Element of the carrier of S
the addF of S . ((0. S),b) is Element of the carrier of S
[(0. S),b] is set
{(0. S),b} is non empty set
{(0. S)} is non empty set
{{(0. S),b},{(0. S)}} is non empty set
the addF of S . [(0. S),b] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
b + x is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (b,x) is Element of the carrier of S
[b,x] is set
{b,x} is non empty set
{b} is non empty set
{{b,x},{b}} is non empty set
the addF of S . [b,x] is set
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
- (1_ F) is Element of the carrier of F
(- (1_ F)) * x is Element of the carrier of S
- x is Element of the carrier of S
(b + x) + (- x) is Element of the carrier of S
the addF of S . ((b + x),(- x)) is Element of the carrier of S
[(b + x),(- x)] is set
{(b + x),(- x)} is non empty set
{(b + x)} is non empty set
{{(b + x),(- x)},{(b + x)}} is non empty set
the addF of S . [(b + x),(- x)] is set
x + (- x) is Element of the carrier of S
the addF of S . (x,(- x)) is Element of the carrier of S
[x,(- x)] is set
{x,(- x)} is non empty set
{x} is non empty set
{{x,(- x)},{x}} is non empty set
the addF of S . [x,(- x)] is set
b + (x + (- x)) is Element of the carrier of S
the addF of S . (b,(x + (- x))) is Element of the carrier of S
[b,(x + (- x))] is set
{b,(x + (- x))} is non empty set
{{b,(x + (- x))},{b}} is non empty set
the addF of S . [b,(x + (- x))] is set
0. S is V53(S) Element of the carrier of S
b + (0. S) is Element of the carrier of S
the addF of S . (b,(0. S)) is Element of the carrier of S
[b,(0. S)] is set
{b,(0. S)} is non empty set
{{b,(0. S)},{b}} is non empty set
the addF of S . [b,(0. S)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
0. F is V53(F) Element of the carrier of F
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of F
x * b is Element of the carrier of S
x * a is Element of the carrier of S
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
z is Element of the carrier of F
z * x is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . (z,x) is Element of the carrier of F
[z,x] is set
{z,x} is non empty set
{z} is non empty set
{{z,x},{z}} is non empty set
the multF of F . [z,x] is set
z * (x * a) is Element of the carrier of S
(1_ F) * a is Element of the carrier of S
z is Element of the carrier of F
z * x is Element of the carrier of F
the multF of F . (z,x) is Element of the carrier of F
[z,x] is set
{z,x} is non empty set
{z} is non empty set
{{z,x},{z}} is non empty set
the multF of F . [z,x] is set
z * (x * b) is Element of the carrier of S
(1_ F) * b is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
- b is Element of the carrier of S
a is Element of the carrier of S
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
- (1_ F) is Element of the carrier of F
(- (1_ F)) * b is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
b - a is Element of the carrier of S
- a is Element of the carrier of S
b + (- a) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (b,(- a)) is Element of the carrier of S
[b,(- a)] is set
{b,(- a)} is non empty set
{b} is non empty set
{{b,(- a)},{b}} is non empty set
the addF of S . [b,(- a)] is set
x is Element of the carrier of S
y is Element of the carrier of S
b - y is Element of the carrier of S
- y is Element of the carrier of S
b + (- y) is Element of the carrier of S
the addF of S . (b,(- y)) is Element of the carrier of S
[b,(- y)] is set
{b,(- y)} is non empty set
{{b,(- y)},{b}} is non empty set
the addF of S . [b,(- y)] is set
a - y is Element of the carrier of S
a + (- y) is Element of the carrier of S
the addF of S . (a,(- y)) is Element of the carrier of S
[a,(- y)] is set
{a,(- y)} is non empty set
{a} is non empty set
{{a,(- y)},{a}} is non empty set
the addF of S . [a,(- y)] is set
- (b - a) is Element of the carrier of S
- b is Element of the carrier of S
(- b) + a is Element of the carrier of S
the addF of S . ((- b),a) is Element of the carrier of S
[(- b),a] is set
{(- b),a} is non empty set
{(- b)} is non empty set
{{(- b),a},{(- b)}} is non empty set
the addF of S . [(- b),a] is set
a + (- b) is Element of the carrier of S
the addF of S . (a,(- b)) is Element of the carrier of S
[a,(- b)] is set
{a,(- b)} is non empty set
{{a,(- b)},{a}} is non empty set
the addF of S . [a,(- b)] is set
(a + (- b)) + (b - y) is Element of the carrier of S
the addF of S . ((a + (- b)),(b - y)) is Element of the carrier of S
[(a + (- b)),(b - y)] is set
{(a + (- b)),(b - y)} is non empty set
{(a + (- b))} is non empty set
{{(a + (- b)),(b - y)},{(a + (- b))}} is non empty set
the addF of S . [(a + (- b)),(b - y)] is set
b + (- y) is Element of the carrier of S
(- b) + (b + (- y)) is Element of the carrier of S
the addF of S . ((- b),(b + (- y))) is Element of the carrier of S
[(- b),(b + (- y))] is set
{(- b),(b + (- y))} is non empty set
{{(- b),(b + (- y))},{(- b)}} is non empty set
the addF of S . [(- b),(b + (- y))] is set
a + ((- b) + (b + (- y))) is Element of the carrier of S
the addF of S . (a,((- b) + (b + (- y)))) is Element of the carrier of S
[a,((- b) + (b + (- y)))] is set
{a,((- b) + (b + (- y)))} is non empty set
{{a,((- b) + (b + (- y)))},{a}} is non empty set
the addF of S . [a,((- b) + (b + (- y)))] is set
(- b) + b is Element of the carrier of S
the addF of S . ((- b),b) is Element of the carrier of S
[(- b),b] is set
{(- b),b} is non empty set
{{(- b),b},{(- b)}} is non empty set
the addF of S . [(- b),b] is set
((- b) + b) + (- y) is Element of the carrier of S
the addF of S . (((- b) + b),(- y)) is Element of the carrier of S
[((- b) + b),(- y)] is set
{((- b) + b),(- y)} is non empty set
{((- b) + b)} is non empty set
{{((- b) + b),(- y)},{((- b) + b)}} is non empty set
the addF of S . [((- b) + b),(- y)] is set
a + (((- b) + b) + (- y)) is Element of the carrier of S
the addF of S . (a,(((- b) + b) + (- y))) is Element of the carrier of S
[a,(((- b) + b) + (- y))] is set
{a,(((- b) + b) + (- y))} is non empty set
{{a,(((- b) + b) + (- y))},{a}} is non empty set
the addF of S . [a,(((- b) + b) + (- y))] is set
0. S is V53(S) Element of the carrier of S
(0. S) + (- y) is Element of the carrier of S
the addF of S . ((0. S),(- y)) is Element of the carrier of S
[(0. S),(- y)] is set
{(0. S),(- y)} is non empty set
{(0. S)} is non empty set
{{(0. S),(- y)},{(0. S)}} is non empty set
the addF of S . [(0. S),(- y)] is set
a + ((0. S) + (- y)) is Element of the carrier of S
the addF of S . (a,((0. S) + (- y))) is Element of the carrier of S
[a,((0. S) + (- y))] is set
{a,((0. S) + (- y))} is non empty set
{{a,((0. S) + (- y))},{a}} is non empty set
the addF of S . [a,((0. S) + (- y))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of F
y * b is Element of the carrier of S
x - (y * b) is Element of the carrier of S
- (y * b) is Element of the carrier of S
x + (- (y * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- (y * b))) is Element of the carrier of S
[x,(- (y * b))] is set
{x,(- (y * b))} is non empty set
{x} is non empty set
{{x,(- (y * b))},{x}} is non empty set
the addF of S . [x,(- (y * b))] is set
z is Element of the carrier of F
z * b is Element of the carrier of S
x - (z * b) is Element of the carrier of S
- (z * b) is Element of the carrier of S
x + (- (z * b)) is Element of the carrier of S
the addF of S . (x,(- (z * b))) is Element of the carrier of S
[x,(- (z * b))] is set
{x,(- (z * b))} is non empty set
{{x,(- (z * b))},{x}} is non empty set
the addF of S . [x,(- (z * b))] is set
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(y * b) - (z * b) is Element of the carrier of S
(y * b) + (- (z * b)) is Element of the carrier of S
the addF of S . ((y * b),(- (z * b))) is Element of the carrier of S
[(y * b),(- (z * b))] is set
{(y * b),(- (z * b))} is non empty set
{(y * b)} is non empty set
{{(y * b),(- (z * b))},{(y * b)}} is non empty set
the addF of S . [(y * b),(- (z * b))] is set
- (1_ F) is Element of the carrier of F
(- (1_ F)) * (z * b) is Element of the carrier of S
(y * b) + ((- (1_ F)) * (z * b)) is Element of the carrier of S
the addF of S . ((y * b),((- (1_ F)) * (z * b))) is Element of the carrier of S
[(y * b),((- (1_ F)) * (z * b))] is set
{(y * b),((- (1_ F)) * (z * b))} is non empty set
{{(y * b),((- (1_ F)) * (z * b))},{(y * b)}} is non empty set
the addF of S . [(y * b),((- (1_ F)) * (z * b))] is set
(- (1_ F)) * z is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((- (1_ F)),z) is Element of the carrier of F
[(- (1_ F)),z] is set
{(- (1_ F)),z} is non empty set
{(- (1_ F))} is non empty set
{{(- (1_ F)),z},{(- (1_ F))}} is non empty set
the multF of F . [(- (1_ F)),z] is set
((- (1_ F)) * z) * b is Element of the carrier of S
(y * b) + (((- (1_ F)) * z) * b) is Element of the carrier of S
the addF of S . ((y * b),(((- (1_ F)) * z) * b)) is Element of the carrier of S
[(y * b),(((- (1_ F)) * z) * b)] is set
{(y * b),(((- (1_ F)) * z) * b)} is non empty set
{{(y * b),(((- (1_ F)) * z) * b)},{(y * b)}} is non empty set
the addF of S . [(y * b),(((- (1_ F)) * z) * b)] is set
z * (1_ F) is Element of the carrier of F
the multF of F . (z,(1_ F)) is Element of the carrier of F
[z,(1_ F)] is set
{z,(1_ F)} is non empty set
{z} is non empty set
{{z,(1_ F)},{z}} is non empty set
the multF of F . [z,(1_ F)] is set
- (z * (1_ F)) is Element of the carrier of F
(- (z * (1_ F))) * b is Element of the carrier of S
(y * b) + ((- (z * (1_ F))) * b) is Element of the carrier of S
the addF of S . ((y * b),((- (z * (1_ F))) * b)) is Element of the carrier of S
[(y * b),((- (z * (1_ F))) * b)] is set
{(y * b),((- (z * (1_ F))) * b)} is non empty set
{{(y * b),((- (z * (1_ F))) * b)},{(y * b)}} is non empty set
the addF of S . [(y * b),((- (z * (1_ F))) * b)] is set
- z is Element of the carrier of F
(- z) * b is Element of the carrier of S
(y * b) + ((- z) * b) is Element of the carrier of S
the addF of S . ((y * b),((- z) * b)) is Element of the carrier of S
[(y * b),((- z) * b)] is set
{(y * b),((- z) * b)} is non empty set
{{(y * b),((- z) * b)},{(y * b)}} is non empty set
the addF of S . [(y * b),((- z) * b)] is set
y + (- z) is Element of the carrier of F
the addF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
the addF of F . (y,(- z)) is Element of the carrier of F
[y,(- z)] is set
{y,(- z)} is non empty set
{y} is non empty set
{{y,(- z)},{y}} is non empty set
the addF of F . [y,(- z)] is set
(y + (- z)) * b is Element of the carrier of S
(y + (- z)) " is Element of the carrier of F
((y + (- z)) ") * ((y + (- z)) * b) is Element of the carrier of S
((y + (- z)) ") * (y + (- z)) is Element of the carrier of F
the multF of F . (((y + (- z)) "),(y + (- z))) is Element of the carrier of F
[((y + (- z)) "),(y + (- z))] is set
{((y + (- z)) "),(y + (- z))} is non empty set
{((y + (- z)) ")} is non empty set
{{((y + (- z)) "),(y + (- z))},{((y + (- z)) ")}} is non empty set
the multF of F . [((y + (- z)) "),(y + (- z))] is set
(((y + (- z)) ") * (y + (- z))) * b is Element of the carrier of S
y - z is Element of the carrier of F
y + (- z) is Element of the carrier of F
0. F is V53(F) Element of the carrier of F
(1_ F) * b is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
b + a is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (b,a) is Element of the carrier of S
[b,a] is set
{b,a} is non empty set
{b} is non empty set
{{b,a},{b}} is non empty set
the addF of S . [b,a] is set
b - a is Element of the carrier of S
- a is Element of the carrier of S
b + (- a) is Element of the carrier of S
the addF of S . (b,(- a)) is Element of the carrier of S
[b,(- a)] is set
{b,(- a)} is non empty set
{{b,(- a)},{b}} is non empty set
the addF of S . [b,(- a)] is set
0. S is V53(S) Element of the carrier of S
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
- (1_ F) is Element of the carrier of F
(- (1_ F)) * b is Element of the carrier of S
- b is Element of the carrier of S
(0. S) + (- b) is Element of the carrier of S
the addF of S . ((0. S),(- b)) is Element of the carrier of S
[(0. S),(- b)] is set
{(0. S),(- b)} is non empty set
{(0. S)} is non empty set
{{(0. S),(- b)},{(0. S)}} is non empty set
the addF of S . [(0. S),(- b)] is set
a + (- a) is Element of the carrier of S
the addF of S . (a,(- a)) is Element of the carrier of S
[a,(- a)] is set
{a,(- a)} is non empty set
{a} is non empty set
{{a,(- a)},{a}} is non empty set
the addF of S . [a,(- a)] is set
(a + (- a)) + (- b) is Element of the carrier of S
the addF of S . ((a + (- a)),(- b)) is Element of the carrier of S
[(a + (- a)),(- b)] is set
{(a + (- a)),(- b)} is non empty set
{(a + (- a))} is non empty set
{{(a + (- a)),(- b)},{(a + (- a))}} is non empty set
the addF of S . [(a + (- a)),(- b)] is set
(- a) - b is Element of the carrier of S
(- a) + (- b) is Element of the carrier of S
the addF of S . ((- a),(- b)) is Element of the carrier of S
[(- a),(- b)] is set
{(- a),(- b)} is non empty set
{(- a)} is non empty set
{{(- a),(- b)},{(- a)}} is non empty set
the addF of S . [(- a),(- b)] is set
a + ((- a) - b) is Element of the carrier of S
the addF of S . (a,((- a) - b)) is Element of the carrier of S
[a,((- a) - b)] is set
{a,((- a) - b)} is non empty set
{{a,((- a) - b)},{a}} is non empty set
the addF of S . [a,((- a) - b)] is set
a - (b + a) is Element of the carrier of S
- (b + a) is Element of the carrier of S
a + (- (b + a)) is Element of the carrier of S
the addF of S . (a,(- (b + a))) is Element of the carrier of S
[a,(- (b + a))] is set
{a,(- (b + a))} is non empty set
{{a,(- (b + a))},{a}} is non empty set
the addF of S . [a,(- (b + a))] is set
a + (0. S) is Element of the carrier of S
the addF of S . (a,(0. S)) is Element of the carrier of S
[a,(0. S)] is set
{a,(0. S)} is non empty set
{{a,(0. S)},{a}} is non empty set
the addF of S . [a,(0. S)] is set
b + (- b) is Element of the carrier of S
the addF of S . (b,(- b)) is Element of the carrier of S
[b,(- b)] is set
{b,(- b)} is non empty set
{{b,(- b)},{b}} is non empty set
the addF of S . [b,(- b)] is set
a + (b + (- b)) is Element of the carrier of S
the addF of S . (a,(b + (- b))) is Element of the carrier of S
[a,(b + (- b))] is set
{a,(b + (- b))} is non empty set
{{a,(b + (- b))},{a}} is non empty set
the addF of S . [a,(b + (- b))] is set
(b + a) - b is Element of the carrier of S
(b + a) + (- b) is Element of the carrier of S
the addF of S . ((b + a),(- b)) is Element of the carrier of S
[(b + a),(- b)] is set
{(b + a),(- b)} is non empty set
{(b + a)} is non empty set
{{(b + a),(- b)},{(b + a)}} is non empty set
the addF of S . [(b + a),(- b)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
(1_ F) + (1_ F) is Element of the carrier of F
the addF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the addF of F . ((1_ F),(1_ F)) is Element of the carrier of F
[(1_ F),(1_ F)] is set
{(1_ F),(1_ F)} is non empty set
{(1_ F)} is non empty set
{{(1_ F),(1_ F)},{(1_ F)}} is non empty set
the addF of F . [(1_ F),(1_ F)] is set
0. F is V53(F) Element of the carrier of F
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
0. S is V53(S) Element of the carrier of S
x is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of S
z is Element of the carrier of S
z + y is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (z,y) is Element of the carrier of S
[z,y] is set
{z,y} is non empty set
{z} is non empty set
{{z,y},{z}} is non empty set
the addF of S . [z,y] is set
z - y is Element of the carrier of S
- y is Element of the carrier of S
z + (- y) is Element of the carrier of S
the addF of S . (z,(- y)) is Element of the carrier of S
[z,(- y)] is set
{z,(- y)} is non empty set
{{z,(- y)},{z}} is non empty set
the addF of S . [z,(- y)] is set
(- y) + z is Element of the carrier of S
the addF of S . ((- y),z) is Element of the carrier of S
[(- y),z] is set
{(- y),z} is non empty set
{(- y)} is non empty set
{{(- y),z},{(- y)}} is non empty set
the addF of S . [(- y),z] is set
(z + y) + ((- y) + z) is Element of the carrier of S
the addF of S . ((z + y),((- y) + z)) is Element of the carrier of S
[(z + y),((- y) + z)] is set
{(z + y),((- y) + z)} is non empty set
{(z + y)} is non empty set
{{(z + y),((- y) + z)},{(z + y)}} is non empty set
the addF of S . [(z + y),((- y) + z)] is set
(z + y) + (- y) is Element of the carrier of S
the addF of S . ((z + y),(- y)) is Element of the carrier of S
[(z + y),(- y)] is set
{(z + y),(- y)} is non empty set
{{(z + y),(- y)},{(z + y)}} is non empty set
the addF of S . [(z + y),(- y)] is set
((z + y) + (- y)) + z is Element of the carrier of S
the addF of S . (((z + y) + (- y)),z) is Element of the carrier of S
[((z + y) + (- y)),z] is set
{((z + y) + (- y)),z} is non empty set
{((z + y) + (- y))} is non empty set
{{((z + y) + (- y)),z},{((z + y) + (- y))}} is non empty set
the addF of S . [((z + y) + (- y)),z] is set
y + (- y) is Element of the carrier of S
the addF of S . (y,(- y)) is Element of the carrier of S
[y,(- y)] is set
{y,(- y)} is non empty set
{y} is non empty set
{{y,(- y)},{y}} is non empty set
the addF of S . [y,(- y)] is set
z + (y + (- y)) is Element of the carrier of S
the addF of S . (z,(y + (- y))) is Element of the carrier of S
[z,(y + (- y))] is set
{z,(y + (- y))} is non empty set
{{z,(y + (- y))},{z}} is non empty set
the addF of S . [z,(y + (- y))] is set
(z + (y + (- y))) + z is Element of the carrier of S
the addF of S . ((z + (y + (- y))),z) is Element of the carrier of S
[(z + (y + (- y))),z] is set
{(z + (y + (- y))),z} is non empty set
{(z + (y + (- y)))} is non empty set
{{(z + (y + (- y))),z},{(z + (y + (- y)))}} is non empty set
the addF of S . [(z + (y + (- y))),z] is set
z + (0. S) is Element of the carrier of S
the addF of S . (z,(0. S)) is Element of the carrier of S
[z,(0. S)] is set
{z,(0. S)} is non empty set
{{z,(0. S)},{z}} is non empty set
the addF of S . [z,(0. S)] is set
(z + (0. S)) + z is Element of the carrier of S
the addF of S . ((z + (0. S)),z) is Element of the carrier of S
[(z + (0. S)),z] is set
{(z + (0. S)),z} is non empty set
{(z + (0. S))} is non empty set
{{(z + (0. S)),z},{(z + (0. S))}} is non empty set
the addF of S . [(z + (0. S)),z] is set
z + z is Element of the carrier of S
the addF of S . (z,z) is Element of the carrier of S
[z,z] is set
{z,z} is non empty set
{{z,z},{z}} is non empty set
the addF of S . [z,z] is set
(1_ F) * z is Element of the carrier of S
((1_ F) * z) + z is Element of the carrier of S
the addF of S . (((1_ F) * z),z) is Element of the carrier of S
[((1_ F) * z),z] is set
{((1_ F) * z),z} is non empty set
{((1_ F) * z)} is non empty set
{{((1_ F) * z),z},{((1_ F) * z)}} is non empty set
the addF of S . [((1_ F) * z),z] is set
((1_ F) * z) + ((1_ F) * z) is Element of the carrier of S
the addF of S . (((1_ F) * z),((1_ F) * z)) is Element of the carrier of S
[((1_ F) * z),((1_ F) * z)] is set
{((1_ F) * z),((1_ F) * z)} is non empty set
{{((1_ F) * z),((1_ F) * z)},{((1_ F) * z)}} is non empty set
the addF of S . [((1_ F) * z),((1_ F) * z)] is set
((1_ F) + (1_ F)) * z is Element of the carrier of S
((1_ F) + (1_ F)) " is Element of the carrier of F
(((1_ F) + (1_ F)) ") * (((1_ F) + (1_ F)) * z) is Element of the carrier of S
(((1_ F) + (1_ F)) ") * ((1_ F) + (1_ F)) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
the multF of F . ((((1_ F) + (1_ F)) "),((1_ F) + (1_ F))) is Element of the carrier of F
[(((1_ F) + (1_ F)) "),((1_ F) + (1_ F))] is set
{(((1_ F) + (1_ F)) "),((1_ F) + (1_ F))} is non empty set
{(((1_ F) + (1_ F)) ")} is non empty set
{{(((1_ F) + (1_ F)) "),((1_ F) + (1_ F))},{(((1_ F) + (1_ F)) ")}} is non empty set
the multF of F . [(((1_ F) + (1_ F)) "),((1_ F) + (1_ F))] is set
((((1_ F) + (1_ F)) ") * ((1_ F) + (1_ F))) * z is Element of the carrier of S
- z is Element of the carrier of S
(- z) + (z + y) is Element of the carrier of S
the addF of S . ((- z),(z + y)) is Element of the carrier of S
[(- z),(z + y)] is set
{(- z),(z + y)} is non empty set
{(- z)} is non empty set
{{(- z),(z + y)},{(- z)}} is non empty set
the addF of S . [(- z),(z + y)] is set
(- z) + z is Element of the carrier of S
the addF of S . ((- z),z) is Element of the carrier of S
[(- z),z] is set
{(- z),z} is non empty set
{{(- z),z},{(- z)}} is non empty set
the addF of S . [(- z),z] is set
((- z) + z) + y is Element of the carrier of S
the addF of S . (((- z) + z),y) is Element of the carrier of S
[((- z) + z),y] is set
{((- z) + z),y} is non empty set
{((- z) + z)} is non empty set
{{((- z) + z),y},{((- z) + z)}} is non empty set
the addF of S . [((- z) + z),y] is set
(0. S) + y is Element of the carrier of S
the addF of S . ((0. S),y) is Element of the carrier of S
[(0. S),y] is set
{(0. S),y} is non empty set
{(0. S)} is non empty set
{{(0. S),y},{(0. S)}} is non empty set
the addF of S . [(0. S),y] is set
y is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
a is Element of the carrier of S
b is Element of the carrier of S
the carrier of F is non empty non trivial set
x is Element of the carrier of S
y is Element of the carrier of F
y * a is Element of the carrier of S
x - (y * a) is Element of the carrier of S
- (y * a) is Element of the carrier of S
x + (- (y * a)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- (y * a))) is Element of the carrier of S
[x,(- (y * a))] is set
{x,(- (y * a))} is non empty set
{x} is non empty set
{{x,(- (y * a))},{x}} is non empty set
the addF of S . [x,(- (y * a))] is set
z is Element of the carrier of F
z * a is Element of the carrier of S
x - (z * a) is Element of the carrier of S
- (z * a) is Element of the carrier of S
x + (- (z * a)) is Element of the carrier of S
the addF of S . (x,(- (z * a))) is Element of the carrier of S
[x,(- (z * a))] is set
{x,(- (z * a))} is non empty set
{{x,(- (z * a))},{x}} is non empty set
the addF of S . [x,(- (z * a))] is set
y is Element of the carrier of F
z is Element of the carrier of F
0F is Element of the carrier of F
0F * a is Element of the carrier of S
x - (0F * a) is Element of the carrier of S
- (0F * a) is Element of the carrier of S
x + (- (0F * a)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- (0F * a))) is Element of the carrier of S
[x,(- (0F * a))] is set
{x,(- (0F * a))} is non empty set
{x} is non empty set
{{x,(- (0F * a))},{x}} is non empty set
the addF of S . [x,(- (0F * a))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{x} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
y is Element of the carrier of F
y * b is Element of the carrier of S
x - (y * b) is Element of the carrier of S
- (y * b) is Element of the carrier of S
x + (- (y * b)) is Element of the carrier of S
the addF of S . (x,(- (y * b))) is Element of the carrier of S
[x,(- (y * b))] is set
{x,(- (y * b))} is non empty set
{{x,(- (y * b))},{x}} is non empty set
the addF of S . [x,(- (y * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
y is Element of the carrier of F
y * x is Element of the carrier of S
(F,S,a,b,(y * x)) is Element of the carrier of F
y * (F,S,a,b,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . (y,(F,S,a,b,x)) is Element of the carrier of F
[y,(F,S,a,b,x)] is set
{y,(F,S,a,b,x)} is non empty set
{y} is non empty set
{{y,(F,S,a,b,x)},{y}} is non empty set
the multF of F . [y,(F,S,a,b,x)] is set
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{x} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
y * (x - ((F,S,a,b,x) * b)) is Element of the carrier of S
y * ((F,S,a,b,x) * b) is Element of the carrier of S
(y * x) - (y * ((F,S,a,b,x) * b)) is Element of the carrier of S
- (y * ((F,S,a,b,x) * b)) is Element of the carrier of S
(y * x) + (- (y * ((F,S,a,b,x) * b))) is Element of the carrier of S
the addF of S . ((y * x),(- (y * ((F,S,a,b,x) * b)))) is Element of the carrier of S
[(y * x),(- (y * ((F,S,a,b,x) * b)))] is set
{(y * x),(- (y * ((F,S,a,b,x) * b)))} is non empty set
{(y * x)} is non empty set
{{(y * x),(- (y * ((F,S,a,b,x) * b)))},{(y * x)}} is non empty set
the addF of S . [(y * x),(- (y * ((F,S,a,b,x) * b)))] is set
(y * (F,S,a,b,x)) * b is Element of the carrier of S
(y * x) - ((y * (F,S,a,b,x)) * b) is Element of the carrier of S
- ((y * (F,S,a,b,x)) * b) is Element of the carrier of S
(y * x) + (- ((y * (F,S,a,b,x)) * b)) is Element of the carrier of S
the addF of S . ((y * x),(- ((y * (F,S,a,b,x)) * b))) is Element of the carrier of S
[(y * x),(- ((y * (F,S,a,b,x)) * b))] is set
{(y * x),(- ((y * (F,S,a,b,x)) * b))} is non empty set
{{(y * x),(- ((y * (F,S,a,b,x)) * b))},{(y * x)}} is non empty set
the addF of S . [(y * x),(- ((y * (F,S,a,b,x)) * b))] is set
(F,S,a,b,(y * x)) * b is Element of the carrier of S
(y * x) - ((F,S,a,b,(y * x)) * b) is Element of the carrier of S
- ((F,S,a,b,(y * x)) * b) is Element of the carrier of S
(y * x) + (- ((F,S,a,b,(y * x)) * b)) is Element of the carrier of S
the addF of S . ((y * x),(- ((F,S,a,b,(y * x)) * b))) is Element of the carrier of S
[(y * x),(- ((F,S,a,b,(y * x)) * b))] is set
{(y * x),(- ((F,S,a,b,(y * x)) * b))} is non empty set
{{(y * x),(- ((F,S,a,b,(y * x)) * b))},{(y * x)}} is non empty set
the addF of S . [(y * x),(- ((F,S,a,b,(y * x)) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
y is Element of the carrier of S
x + y is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,y) is Element of the carrier of S
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of S . [x,y] is set
(F,S,a,b,(x + y)) is Element of the carrier of F
(F,S,a,b,y) is Element of the carrier of F
(F,S,a,b,x) + (F,S,a,b,y) is Element of the carrier of F
the addF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the addF of F . ((F,S,a,b,x),(F,S,a,b,y)) is Element of the carrier of F
[(F,S,a,b,x),(F,S,a,b,y)] is set
{(F,S,a,b,x),(F,S,a,b,y)} is non empty set
{(F,S,a,b,x)} is non empty set
{{(F,S,a,b,x),(F,S,a,b,y)},{(F,S,a,b,x)}} is non empty set
the addF of F . [(F,S,a,b,x),(F,S,a,b,y)] is set
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
(F,S,a,b,y) * b is Element of the carrier of S
y - ((F,S,a,b,y) * b) is Element of the carrier of S
- ((F,S,a,b,y) * b) is Element of the carrier of S
y + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[y,(- ((F,S,a,b,y) * b))] is set
{y,(- ((F,S,a,b,y) * b))} is non empty set
{y} is non empty set
{{y,(- ((F,S,a,b,y) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,b,y) * b))] is set
(x - ((F,S,a,b,x) * b)) + (y - ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . ((x - ((F,S,a,b,x) * b)),(y - ((F,S,a,b,y) * b))) is Element of the carrier of S
[(x - ((F,S,a,b,x) * b)),(y - ((F,S,a,b,y) * b))] is set
{(x - ((F,S,a,b,x) * b)),(y - ((F,S,a,b,y) * b))} is non empty set
{(x - ((F,S,a,b,x) * b))} is non empty set
{{(x - ((F,S,a,b,x) * b)),(y - ((F,S,a,b,y) * b))},{(x - ((F,S,a,b,x) * b))}} is non empty set
the addF of S . [(x - ((F,S,a,b,x) * b)),(y - ((F,S,a,b,y) * b))] is set
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
(x + (- ((F,S,a,b,x) * b))) + (y - ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . ((x + (- ((F,S,a,b,x) * b))),(y - ((F,S,a,b,y) * b))) is Element of the carrier of S
[(x + (- ((F,S,a,b,x) * b))),(y - ((F,S,a,b,y) * b))] is set
{(x + (- ((F,S,a,b,x) * b))),(y - ((F,S,a,b,y) * b))} is non empty set
{(x + (- ((F,S,a,b,x) * b)))} is non empty set
{{(x + (- ((F,S,a,b,x) * b))),(y - ((F,S,a,b,y) * b))},{(x + (- ((F,S,a,b,x) * b)))}} is non empty set
the addF of S . [(x + (- ((F,S,a,b,x) * b))),(y - ((F,S,a,b,y) * b))] is set
y + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
(x + (- ((F,S,a,b,x) * b))) + (y + (- ((F,S,a,b,y) * b))) is Element of the carrier of S
the addF of S . ((x + (- ((F,S,a,b,x) * b))),(y + (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
[(x + (- ((F,S,a,b,x) * b))),(y + (- ((F,S,a,b,y) * b)))] is set
{(x + (- ((F,S,a,b,x) * b))),(y + (- ((F,S,a,b,y) * b)))} is non empty set
{{(x + (- ((F,S,a,b,x) * b))),(y + (- ((F,S,a,b,y) * b)))},{(x + (- ((F,S,a,b,x) * b)))}} is non empty set
the addF of S . [(x + (- ((F,S,a,b,x) * b))),(y + (- ((F,S,a,b,y) * b)))] is set
(- ((F,S,a,b,x) * b)) + x is Element of the carrier of S
the addF of S . ((- ((F,S,a,b,x) * b)),x) is Element of the carrier of S
[(- ((F,S,a,b,x) * b)),x] is set
{(- ((F,S,a,b,x) * b)),x} is non empty set
{(- ((F,S,a,b,x) * b))} is non empty set
{{(- ((F,S,a,b,x) * b)),x},{(- ((F,S,a,b,x) * b))}} is non empty set
the addF of S . [(- ((F,S,a,b,x) * b)),x] is set
((- ((F,S,a,b,x) * b)) + x) + y is Element of the carrier of S
the addF of S . (((- ((F,S,a,b,x) * b)) + x),y) is Element of the carrier of S
[((- ((F,S,a,b,x) * b)) + x),y] is set
{((- ((F,S,a,b,x) * b)) + x),y} is non empty set
{((- ((F,S,a,b,x) * b)) + x)} is non empty set
{{((- ((F,S,a,b,x) * b)) + x),y},{((- ((F,S,a,b,x) * b)) + x)}} is non empty set
the addF of S . [((- ((F,S,a,b,x) * b)) + x),y] is set
(((- ((F,S,a,b,x) * b)) + x) + y) + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . ((((- ((F,S,a,b,x) * b)) + x) + y),(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[(((- ((F,S,a,b,x) * b)) + x) + y),(- ((F,S,a,b,y) * b))] is set
{(((- ((F,S,a,b,x) * b)) + x) + y),(- ((F,S,a,b,y) * b))} is non empty set
{(((- ((F,S,a,b,x) * b)) + x) + y)} is non empty set
{{(((- ((F,S,a,b,x) * b)) + x) + y),(- ((F,S,a,b,y) * b))},{(((- ((F,S,a,b,x) * b)) + x) + y)}} is non empty set
the addF of S . [(((- ((F,S,a,b,x) * b)) + x) + y),(- ((F,S,a,b,y) * b))] is set
(x + y) + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . ((x + y),(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[(x + y),(- ((F,S,a,b,x) * b))] is set
{(x + y),(- ((F,S,a,b,x) * b))} is non empty set
{(x + y)} is non empty set
{{(x + y),(- ((F,S,a,b,x) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),(- ((F,S,a,b,x) * b))] is set
((x + y) + (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . (((x + y) + (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[((x + y) + (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))] is set
{((x + y) + (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))} is non empty set
{((x + y) + (- ((F,S,a,b,x) * b)))} is non empty set
{{((x + y) + (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))},{((x + y) + (- ((F,S,a,b,x) * b)))}} is non empty set
the addF of S . [((x + y) + (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))] is set
(- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . ((- ((F,S,a,b,x) * b)),(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[(- ((F,S,a,b,x) * b)),(- ((F,S,a,b,y) * b))] is set
{(- ((F,S,a,b,x) * b)),(- ((F,S,a,b,y) * b))} is non empty set
{{(- ((F,S,a,b,x) * b)),(- ((F,S,a,b,y) * b))},{(- ((F,S,a,b,x) * b))}} is non empty set
the addF of S . [(- ((F,S,a,b,x) * b)),(- ((F,S,a,b,y) * b))] is set
(x + y) + ((- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b))) is Element of the carrier of S
the addF of S . ((x + y),((- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
[(x + y),((- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b)))] is set
{(x + y),((- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b)))} is non empty set
{{(x + y),((- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b)))},{(x + y)}} is non empty set
the addF of S . [(x + y),((- ((F,S,a,b,x) * b)) + (- ((F,S,a,b,y) * b)))] is set
(1_ F) * (- ((F,S,a,b,x) * b)) is Element of the carrier of S
((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . (((1_ F) * (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[((1_ F) * (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))] is set
{((1_ F) * (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))} is non empty set
{((1_ F) * (- ((F,S,a,b,x) * b)))} is non empty set
{{((1_ F) * (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))},{((1_ F) * (- ((F,S,a,b,x) * b)))}} is non empty set
the addF of S . [((1_ F) * (- ((F,S,a,b,x) * b))),(- ((F,S,a,b,y) * b))] is set
(x + y) + (((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b))) is Element of the carrier of S
the addF of S . ((x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
[(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)))] is set
{(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)))} is non empty set
{{(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)))},{(x + y)}} is non empty set
the addF of S . [(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + (- ((F,S,a,b,y) * b)))] is set
(1_ F) * (- ((F,S,a,b,y) * b)) is Element of the carrier of S
((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b))) is Element of the carrier of S
the addF of S . (((1_ F) * (- ((F,S,a,b,x) * b))),((1_ F) * (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
[((1_ F) * (- ((F,S,a,b,x) * b))),((1_ F) * (- ((F,S,a,b,y) * b)))] is set
{((1_ F) * (- ((F,S,a,b,x) * b))),((1_ F) * (- ((F,S,a,b,y) * b)))} is non empty set
{{((1_ F) * (- ((F,S,a,b,x) * b))),((1_ F) * (- ((F,S,a,b,y) * b)))},{((1_ F) * (- ((F,S,a,b,x) * b)))}} is non empty set
the addF of S . [((1_ F) * (- ((F,S,a,b,x) * b))),((1_ F) * (- ((F,S,a,b,y) * b)))] is set
(x + y) + (((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
the addF of S . ((x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b))))) is Element of the carrier of S
[(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b))))] is set
{(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b))))} is non empty set
{{(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b))))},{(x + y)}} is non empty set
the addF of S . [(x + y),(((1_ F) * (- ((F,S,a,b,x) * b))) + ((1_ F) * (- ((F,S,a,b,y) * b))))] is set
- (F,S,a,b,x) is Element of the carrier of F
(- (F,S,a,b,x)) * b is Element of the carrier of S
(1_ F) * ((- (F,S,a,b,x)) * b) is Element of the carrier of S
((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b))) is Element of the carrier of S
the addF of S . (((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
[((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * (- ((F,S,a,b,y) * b)))] is set
{((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * (- ((F,S,a,b,y) * b)))} is non empty set
{((1_ F) * ((- (F,S,a,b,x)) * b))} is non empty set
{{((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * (- ((F,S,a,b,y) * b)))},{((1_ F) * ((- (F,S,a,b,x)) * b))}} is non empty set
the addF of S . [((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * (- ((F,S,a,b,y) * b)))] is set
(x + y) + (((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b)))) is Element of the carrier of S
the addF of S . ((x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b))))) is Element of the carrier of S
[(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b))))] is set
{(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b))))} is non empty set
{{(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b))))},{(x + y)}} is non empty set
the addF of S . [(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * (- ((F,S,a,b,y) * b))))] is set
- (F,S,a,b,y) is Element of the carrier of F
(- (F,S,a,b,y)) * b is Element of the carrier of S
(1_ F) * ((- (F,S,a,b,y)) * b) is Element of the carrier of S
((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b)) is Element of the carrier of S
the addF of S . (((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * ((- (F,S,a,b,y)) * b))) is Element of the carrier of S
[((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * ((- (F,S,a,b,y)) * b))] is set
{((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * ((- (F,S,a,b,y)) * b))} is non empty set
{{((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * ((- (F,S,a,b,y)) * b))},{((1_ F) * ((- (F,S,a,b,x)) * b))}} is non empty set
the addF of S . [((1_ F) * ((- (F,S,a,b,x)) * b)),((1_ F) * ((- (F,S,a,b,y)) * b))] is set
(x + y) + (((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b))) is Element of the carrier of S
the addF of S . ((x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b)))) is Element of the carrier of S
[(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b)))] is set
{(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b)))} is non empty set
{{(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b)))},{(x + y)}} is non empty set
the addF of S . [(x + y),(((1_ F) * ((- (F,S,a,b,x)) * b)) + ((1_ F) * ((- (F,S,a,b,y)) * b)))] is set
(1_ F) * (- (F,S,a,b,x)) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
the multF of F . ((1_ F),(- (F,S,a,b,x))) is Element of the carrier of F
[(1_ F),(- (F,S,a,b,x))] is set
{(1_ F),(- (F,S,a,b,x))} is non empty set
{(1_ F)} is non empty set
{{(1_ F),(- (F,S,a,b,x))},{(1_ F)}} is non empty set
the multF of F . [(1_ F),(- (F,S,a,b,x))] is set
((1_ F) * (- (F,S,a,b,x))) * b is Element of the carrier of S
(((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b)) is Element of the carrier of S
the addF of S . ((((1_ F) * (- (F,S,a,b,x))) * b),((1_ F) * ((- (F,S,a,b,y)) * b))) is Element of the carrier of S
[(((1_ F) * (- (F,S,a,b,x))) * b),((1_ F) * ((- (F,S,a,b,y)) * b))] is set
{(((1_ F) * (- (F,S,a,b,x))) * b),((1_ F) * ((- (F,S,a,b,y)) * b))} is non empty set
{(((1_ F) * (- (F,S,a,b,x))) * b)} is non empty set
{{(((1_ F) * (- (F,S,a,b,x))) * b),((1_ F) * ((- (F,S,a,b,y)) * b))},{(((1_ F) * (- (F,S,a,b,x))) * b)}} is non empty set
the addF of S . [(((1_ F) * (- (F,S,a,b,x))) * b),((1_ F) * ((- (F,S,a,b,y)) * b))] is set
(x + y) + ((((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b))) is Element of the carrier of S
the addF of S . ((x + y),((((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b)))) is Element of the carrier of S
[(x + y),((((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b)))] is set
{(x + y),((((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b)))} is non empty set
{{(x + y),((((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b)))},{(x + y)}} is non empty set
the addF of S . [(x + y),((((1_ F) * (- (F,S,a,b,x))) * b) + ((1_ F) * ((- (F,S,a,b,y)) * b)))] is set
(- (F,S,a,b,x)) * (1_ F) is Element of the carrier of F
the multF of F . ((- (F,S,a,b,x)),(1_ F)) is Element of the carrier of F
[(- (F,S,a,b,x)),(1_ F)] is set
{(- (F,S,a,b,x)),(1_ F)} is non empty set
{(- (F,S,a,b,x))} is non empty set
{{(- (F,S,a,b,x)),(1_ F)},{(- (F,S,a,b,x))}} is non empty set
the multF of F . [(- (F,S,a,b,x)),(1_ F)] is set
((- (F,S,a,b,x)) * (1_ F)) * b is Element of the carrier of S
(1_ F) * (- (F,S,a,b,y)) is Element of the carrier of F
the multF of F . ((1_ F),(- (F,S,a,b,y))) is Element of the carrier of F
[(1_ F),(- (F,S,a,b,y))] is set
{(1_ F),(- (F,S,a,b,y))} is non empty set
{{(1_ F),(- (F,S,a,b,y))},{(1_ F)}} is non empty set
the multF of F . [(1_ F),(- (F,S,a,b,y))] is set
((1_ F) * (- (F,S,a,b,y))) * b is Element of the carrier of S
(((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b) is Element of the carrier of S
the addF of S . ((((- (F,S,a,b,x)) * (1_ F)) * b),(((1_ F) * (- (F,S,a,b,y))) * b)) is Element of the carrier of S
[(((- (F,S,a,b,x)) * (1_ F)) * b),(((1_ F) * (- (F,S,a,b,y))) * b)] is set
{(((- (F,S,a,b,x)) * (1_ F)) * b),(((1_ F) * (- (F,S,a,b,y))) * b)} is non empty set
{(((- (F,S,a,b,x)) * (1_ F)) * b)} is non empty set
{{(((- (F,S,a,b,x)) * (1_ F)) * b),(((1_ F) * (- (F,S,a,b,y))) * b)},{(((- (F,S,a,b,x)) * (1_ F)) * b)}} is non empty set
the addF of S . [(((- (F,S,a,b,x)) * (1_ F)) * b),(((1_ F) * (- (F,S,a,b,y))) * b)] is set
(x + y) + ((((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b)) is Element of the carrier of S
the addF of S . ((x + y),((((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b))) is Element of the carrier of S
[(x + y),((((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b))] is set
{(x + y),((((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b))} is non empty set
{{(x + y),((((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),((((- (F,S,a,b,x)) * (1_ F)) * b) + (((1_ F) * (- (F,S,a,b,y))) * b))] is set
(- (F,S,a,b,y)) * (1_ F) is Element of the carrier of F
the multF of F . ((- (F,S,a,b,y)),(1_ F)) is Element of the carrier of F
[(- (F,S,a,b,y)),(1_ F)] is set
{(- (F,S,a,b,y)),(1_ F)} is non empty set
{(- (F,S,a,b,y))} is non empty set
{{(- (F,S,a,b,y)),(1_ F)},{(- (F,S,a,b,y))}} is non empty set
the multF of F . [(- (F,S,a,b,y)),(1_ F)] is set
((- (F,S,a,b,y)) * (1_ F)) * b is Element of the carrier of S
((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b) is Element of the carrier of S
the addF of S . (((- (F,S,a,b,x)) * b),(((- (F,S,a,b,y)) * (1_ F)) * b)) is Element of the carrier of S
[((- (F,S,a,b,x)) * b),(((- (F,S,a,b,y)) * (1_ F)) * b)] is set
{((- (F,S,a,b,x)) * b),(((- (F,S,a,b,y)) * (1_ F)) * b)} is non empty set
{((- (F,S,a,b,x)) * b)} is non empty set
{{((- (F,S,a,b,x)) * b),(((- (F,S,a,b,y)) * (1_ F)) * b)},{((- (F,S,a,b,x)) * b)}} is non empty set
the addF of S . [((- (F,S,a,b,x)) * b),(((- (F,S,a,b,y)) * (1_ F)) * b)] is set
(x + y) + (((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b)) is Element of the carrier of S
the addF of S . ((x + y),(((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b))) is Element of the carrier of S
[(x + y),(((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b))] is set
{(x + y),(((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b))} is non empty set
{{(x + y),(((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),(((- (F,S,a,b,x)) * b) + (((- (F,S,a,b,y)) * (1_ F)) * b))] is set
((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b) is Element of the carrier of S
the addF of S . (((- (F,S,a,b,x)) * b),((- (F,S,a,b,y)) * b)) is Element of the carrier of S
[((- (F,S,a,b,x)) * b),((- (F,S,a,b,y)) * b)] is set
{((- (F,S,a,b,x)) * b),((- (F,S,a,b,y)) * b)} is non empty set
{{((- (F,S,a,b,x)) * b),((- (F,S,a,b,y)) * b)},{((- (F,S,a,b,x)) * b)}} is non empty set
the addF of S . [((- (F,S,a,b,x)) * b),((- (F,S,a,b,y)) * b)] is set
(x + y) + (((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b)) is Element of the carrier of S
the addF of S . ((x + y),(((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b))) is Element of the carrier of S
[(x + y),(((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b))] is set
{(x + y),(((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b))} is non empty set
{{(x + y),(((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),(((- (F,S,a,b,x)) * b) + ((- (F,S,a,b,y)) * b))] is set
(- (F,S,a,b,x)) + (- (F,S,a,b,y)) is Element of the carrier of F
the addF of F . ((- (F,S,a,b,x)),(- (F,S,a,b,y))) is Element of the carrier of F
[(- (F,S,a,b,x)),(- (F,S,a,b,y))] is set
{(- (F,S,a,b,x)),(- (F,S,a,b,y))} is non empty set
{{(- (F,S,a,b,x)),(- (F,S,a,b,y))},{(- (F,S,a,b,x))}} is non empty set
the addF of F . [(- (F,S,a,b,x)),(- (F,S,a,b,y))] is set
((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b is Element of the carrier of S
(x + y) + (((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b) is Element of the carrier of S
the addF of S . ((x + y),(((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b)) is Element of the carrier of S
[(x + y),(((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b)] is set
{(x + y),(((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b)} is non empty set
{{(x + y),(((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b)},{(x + y)}} is non empty set
the addF of S . [(x + y),(((- (F,S,a,b,x)) + (- (F,S,a,b,y))) * b)] is set
- ((F,S,a,b,x) + (F,S,a,b,y)) is Element of the carrier of F
(- ((F,S,a,b,x) + (F,S,a,b,y))) * b is Element of the carrier of S
(x + y) + ((- ((F,S,a,b,x) + (F,S,a,b,y))) * b) is Element of the carrier of S
the addF of S . ((x + y),((- ((F,S,a,b,x) + (F,S,a,b,y))) * b)) is Element of the carrier of S
[(x + y),((- ((F,S,a,b,x) + (F,S,a,b,y))) * b)] is set
{(x + y),((- ((F,S,a,b,x) + (F,S,a,b,y))) * b)} is non empty set
{{(x + y),((- ((F,S,a,b,x) + (F,S,a,b,y))) * b)},{(x + y)}} is non empty set
the addF of S . [(x + y),((- ((F,S,a,b,x) + (F,S,a,b,y))) * b)] is set
((F,S,a,b,x) + (F,S,a,b,y)) * b is Element of the carrier of S
(x + y) - (((F,S,a,b,x) + (F,S,a,b,y)) * b) is Element of the carrier of S
- (((F,S,a,b,x) + (F,S,a,b,y)) * b) is Element of the carrier of S
(x + y) + (- (((F,S,a,b,x) + (F,S,a,b,y)) * b)) is Element of the carrier of S
the addF of S . ((x + y),(- (((F,S,a,b,x) + (F,S,a,b,y)) * b))) is Element of the carrier of S
[(x + y),(- (((F,S,a,b,x) + (F,S,a,b,y)) * b))] is set
{(x + y),(- (((F,S,a,b,x) + (F,S,a,b,y)) * b))} is non empty set
{{(x + y),(- (((F,S,a,b,x) + (F,S,a,b,y)) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),(- (((F,S,a,b,x) + (F,S,a,b,y)) * b))] is set
(F,S,a,b,(x + y)) * b is Element of the carrier of S
(x + y) - ((F,S,a,b,(x + y)) * b) is Element of the carrier of S
- ((F,S,a,b,(x + y)) * b) is Element of the carrier of S
(x + y) + (- ((F,S,a,b,(x + y)) * b)) is Element of the carrier of S
the addF of S . ((x + y),(- ((F,S,a,b,(x + y)) * b))) is Element of the carrier of S
[(x + y),(- ((F,S,a,b,(x + y)) * b))] is set
{(x + y),(- ((F,S,a,b,(x + y)) * b))} is non empty set
{{(x + y),(- ((F,S,a,b,(x + y)) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),(- ((F,S,a,b,(x + y)) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
0. F is V53(F) Element of the carrier of F
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
y is Element of the carrier of F
y * b is Element of the carrier of S
(F,S,a,(y * b),x) is Element of the carrier of F
y " is Element of the carrier of F
(y ") * (F,S,a,b,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((y "),(F,S,a,b,x)) is Element of the carrier of F
[(y "),(F,S,a,b,x)] is set
{(y "),(F,S,a,b,x)} is non empty set
{(y ")} is non empty set
{{(y "),(F,S,a,b,x)},{(y ")}} is non empty set
the multF of F . [(y "),(F,S,a,b,x)] is set
(F,S,a,(y * b),x) * (y * b) is Element of the carrier of S
x - ((F,S,a,(y * b),x) * (y * b)) is Element of the carrier of S
- ((F,S,a,(y * b),x) * (y * b)) is Element of the carrier of S
x + (- ((F,S,a,(y * b),x) * (y * b))) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- ((F,S,a,(y * b),x) * (y * b)))) is Element of the carrier of S
[x,(- ((F,S,a,(y * b),x) * (y * b)))] is set
{x,(- ((F,S,a,(y * b),x) * (y * b)))} is non empty set
{x} is non empty set
{{x,(- ((F,S,a,(y * b),x) * (y * b)))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,(y * b),x) * (y * b)))] is set
(F,S,a,(y * b),x) * y is Element of the carrier of F
the multF of F . ((F,S,a,(y * b),x),y) is Element of the carrier of F
[(F,S,a,(y * b),x),y] is set
{(F,S,a,(y * b),x),y} is non empty set
{(F,S,a,(y * b),x)} is non empty set
{{(F,S,a,(y * b),x),y},{(F,S,a,(y * b),x)}} is non empty set
the multF of F . [(F,S,a,(y * b),x),y] is set
((F,S,a,(y * b),x) * y) * b is Element of the carrier of S
x - (((F,S,a,(y * b),x) * y) * b) is Element of the carrier of S
- (((F,S,a,(y * b),x) * y) * b) is Element of the carrier of S
x + (- (((F,S,a,(y * b),x) * y) * b)) is Element of the carrier of S
the addF of S . (x,(- (((F,S,a,(y * b),x) * y) * b))) is Element of the carrier of S
[x,(- (((F,S,a,(y * b),x) * y) * b))] is set
{x,(- (((F,S,a,(y * b),x) * y) * b))} is non empty set
{{x,(- (((F,S,a,(y * b),x) * y) * b))},{x}} is non empty set
the addF of S . [x,(- (((F,S,a,(y * b),x) * y) * b))] is set
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
(F,S,a,b,x) * (y ") is Element of the carrier of F
the multF of F . ((F,S,a,b,x),(y ")) is Element of the carrier of F
[(F,S,a,b,x),(y ")] is set
{(F,S,a,b,x),(y ")} is non empty set
{(F,S,a,b,x)} is non empty set
{{(F,S,a,b,x),(y ")},{(F,S,a,b,x)}} is non empty set
the multF of F . [(F,S,a,b,x),(y ")] is set
((F,S,a,(y * b),x) * y) * (y ") is Element of the carrier of F
the multF of F . (((F,S,a,(y * b),x) * y),(y ")) is Element of the carrier of F
[((F,S,a,(y * b),x) * y),(y ")] is set
{((F,S,a,(y * b),x) * y),(y ")} is non empty set
{((F,S,a,(y * b),x) * y)} is non empty set
{{((F,S,a,(y * b),x) * y),(y ")},{((F,S,a,(y * b),x) * y)}} is non empty set
the multF of F . [((F,S,a,(y * b),x) * y),(y ")] is set
y * (y ") is Element of the carrier of F
the multF of F . (y,(y ")) is Element of the carrier of F
[y,(y ")] is set
{y,(y ")} is non empty set
{y} is non empty set
{{y,(y ")},{y}} is non empty set
the multF of F . [y,(y ")] is set
(F,S,a,(y * b),x) * (y * (y ")) is Element of the carrier of F
the multF of F . ((F,S,a,(y * b),x),(y * (y "))) is Element of the carrier of F
[(F,S,a,(y * b),x),(y * (y "))] is set
{(F,S,a,(y * b),x),(y * (y "))} is non empty set
{{(F,S,a,(y * b),x),(y * (y "))},{(F,S,a,(y * b),x)}} is non empty set
the multF of F . [(F,S,a,(y * b),x),(y * (y "))] is set
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(F,S,a,(y * b),x) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,a,(y * b),x),(1_ F)) is Element of the carrier of F
[(F,S,a,(y * b),x),(1_ F)] is set
{(F,S,a,(y * b),x),(1_ F)} is non empty set
{{(F,S,a,(y * b),x),(1_ F)},{(F,S,a,(y * b),x)}} is non empty set
the multF of F . [(F,S,a,(y * b),x),(1_ F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
0. F is V53(F) Element of the carrier of F
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
y is Element of the carrier of F
y * a is Element of the carrier of S
(F,S,(y * a),b,x) is Element of the carrier of F
(F,S,(y * a),b,x) * b is Element of the carrier of S
x - ((F,S,(y * a),b,x) * b) is Element of the carrier of S
- ((F,S,(y * a),b,x) * b) is Element of the carrier of S
x + (- ((F,S,(y * a),b,x) * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- ((F,S,(y * a),b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,(y * a),b,x) * b))] is set
{x,(- ((F,S,(y * a),b,x) * b))} is non empty set
{x} is non empty set
{{x,(- ((F,S,(y * a),b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,(y * a),b,x) * b))] is set
y " is Element of the carrier of F
(y ") * (y * a) is Element of the carrier of S
(y ") * y is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((y "),y) is Element of the carrier of F
[(y "),y] is set
{(y "),y} is non empty set
{(y ")} is non empty set
{{(y "),y},{(y ")}} is non empty set
the multF of F . [(y "),y] is set
((y ") * y) * a is Element of the carrier of S
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(1_ F) * a is Element of the carrier of S
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
b + x is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (b,x) is Element of the carrier of S
[b,x] is set
{b,x} is non empty set
{b} is non empty set
{{b,x},{b}} is non empty set
the addF of S . [b,x] is set
y is Element of the carrier of S
(F,S,a,(b + x),y) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,a,b,y) is Element of the carrier of F
y + x is Element of the carrier of S
the addF of S . (y,x) is Element of the carrier of S
[y,x] is set
{y,x} is non empty set
{y} is non empty set
{{y,x},{y}} is non empty set
the addF of S . [y,x] is set
(F,S,a,b,(y + x)) is Element of the carrier of F
0. S is V53(S) Element of the carrier of S
(F,S,a,(b + x),y) * (b + x) is Element of the carrier of S
y - ((F,S,a,(b + x),y) * (b + x)) is Element of the carrier of S
- ((F,S,a,(b + x),y) * (b + x)) is Element of the carrier of S
y + (- ((F,S,a,(b + x),y) * (b + x))) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,(b + x),y) * (b + x)))) is Element of the carrier of S
[y,(- ((F,S,a,(b + x),y) * (b + x)))] is set
{y,(- ((F,S,a,(b + x),y) * (b + x)))} is non empty set
{{y,(- ((F,S,a,(b + x),y) * (b + x)))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,(b + x),y) * (b + x)))] is set
(F,S,a,(b + x),y) * b is Element of the carrier of S
(F,S,a,(b + x),y) * x is Element of the carrier of S
((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x) is Element of the carrier of S
the addF of S . (((F,S,a,(b + x),y) * b),((F,S,a,(b + x),y) * x)) is Element of the carrier of S
[((F,S,a,(b + x),y) * b),((F,S,a,(b + x),y) * x)] is set
{((F,S,a,(b + x),y) * b),((F,S,a,(b + x),y) * x)} is non empty set
{((F,S,a,(b + x),y) * b)} is non empty set
{{((F,S,a,(b + x),y) * b),((F,S,a,(b + x),y) * x)},{((F,S,a,(b + x),y) * b)}} is non empty set
the addF of S . [((F,S,a,(b + x),y) * b),((F,S,a,(b + x),y) * x)] is set
y - (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)) is Element of the carrier of S
- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)) is Element of the carrier of S
y + (- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x))) is Element of the carrier of S
the addF of S . (y,(- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)))) is Element of the carrier of S
[y,(- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)))] is set
{y,(- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)))} is non empty set
{{y,(- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)))},{y}} is non empty set
the addF of S . [y,(- (((F,S,a,(b + x),y) * b) + ((F,S,a,(b + x),y) * x)))] is set
y - ((F,S,a,(b + x),y) * b) is Element of the carrier of S
- ((F,S,a,(b + x),y) * b) is Element of the carrier of S
y + (- ((F,S,a,(b + x),y) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,(b + x),y) * b))) is Element of the carrier of S
[y,(- ((F,S,a,(b + x),y) * b))] is set
{y,(- ((F,S,a,(b + x),y) * b))} is non empty set
{{y,(- ((F,S,a,(b + x),y) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,(b + x),y) * b))] is set
(y - ((F,S,a,(b + x),y) * b)) - ((F,S,a,(b + x),y) * x) is Element of the carrier of S
- ((F,S,a,(b + x),y) * x) is Element of the carrier of S
(y - ((F,S,a,(b + x),y) * b)) + (- ((F,S,a,(b + x),y) * x)) is Element of the carrier of S
the addF of S . ((y - ((F,S,a,(b + x),y) * b)),(- ((F,S,a,(b + x),y) * x))) is Element of the carrier of S
[(y - ((F,S,a,(b + x),y) * b)),(- ((F,S,a,(b + x),y) * x))] is set
{(y - ((F,S,a,(b + x),y) * b)),(- ((F,S,a,(b + x),y) * x))} is non empty set
{(y - ((F,S,a,(b + x),y) * b))} is non empty set
{{(y - ((F,S,a,(b + x),y) * b)),(- ((F,S,a,(b + x),y) * x))},{(y - ((F,S,a,(b + x),y) * b))}} is non empty set
the addF of S . [(y - ((F,S,a,(b + x),y) * b)),(- ((F,S,a,(b + x),y) * x))] is set
(F,S,a,b,(y + x)) * b is Element of the carrier of S
(y + x) - ((F,S,a,b,(y + x)) * b) is Element of the carrier of S
- ((F,S,a,b,(y + x)) * b) is Element of the carrier of S
(y + x) + (- ((F,S,a,b,(y + x)) * b)) is Element of the carrier of S
the addF of S . ((y + x),(- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
[(y + x),(- ((F,S,a,b,(y + x)) * b))] is set
{(y + x),(- ((F,S,a,b,(y + x)) * b))} is non empty set
{(y + x)} is non empty set
{{(y + x),(- ((F,S,a,b,(y + x)) * b))},{(y + x)}} is non empty set
the addF of S . [(y + x),(- ((F,S,a,b,(y + x)) * b))] is set
- x is Element of the carrier of S
x + y is Element of the carrier of S
the addF of S . (x,y) is Element of the carrier of S
[x,y] is set
{x,y} is non empty set
{x} is non empty set
{{x,y},{x}} is non empty set
the addF of S . [x,y] is set
(x + y) + (- ((F,S,a,b,(y + x)) * b)) is Element of the carrier of S
the addF of S . ((x + y),(- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
[(x + y),(- ((F,S,a,b,(y + x)) * b))] is set
{(x + y),(- ((F,S,a,b,(y + x)) * b))} is non empty set
{(x + y)} is non empty set
{{(x + y),(- ((F,S,a,b,(y + x)) * b))},{(x + y)}} is non empty set
the addF of S . [(x + y),(- ((F,S,a,b,(y + x)) * b))] is set
(- x) + ((x + y) + (- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
the addF of S . ((- x),((x + y) + (- ((F,S,a,b,(y + x)) * b)))) is Element of the carrier of S
[(- x),((x + y) + (- ((F,S,a,b,(y + x)) * b)))] is set
{(- x),((x + y) + (- ((F,S,a,b,(y + x)) * b)))} is non empty set
{(- x)} is non empty set
{{(- x),((x + y) + (- ((F,S,a,b,(y + x)) * b)))},{(- x)}} is non empty set
the addF of S . [(- x),((x + y) + (- ((F,S,a,b,(y + x)) * b)))] is set
y + (- ((F,S,a,b,(y + x)) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
[y,(- ((F,S,a,b,(y + x)) * b))] is set
{y,(- ((F,S,a,b,(y + x)) * b))} is non empty set
{{y,(- ((F,S,a,b,(y + x)) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,b,(y + x)) * b))] is set
x + (y + (- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
the addF of S . (x,(y + (- ((F,S,a,b,(y + x)) * b)))) is Element of the carrier of S
[x,(y + (- ((F,S,a,b,(y + x)) * b)))] is set
{x,(y + (- ((F,S,a,b,(y + x)) * b)))} is non empty set
{{x,(y + (- ((F,S,a,b,(y + x)) * b)))},{x}} is non empty set
the addF of S . [x,(y + (- ((F,S,a,b,(y + x)) * b)))] is set
(- x) + (x + (y + (- ((F,S,a,b,(y + x)) * b)))) is Element of the carrier of S
the addF of S . ((- x),(x + (y + (- ((F,S,a,b,(y + x)) * b))))) is Element of the carrier of S
[(- x),(x + (y + (- ((F,S,a,b,(y + x)) * b))))] is set
{(- x),(x + (y + (- ((F,S,a,b,(y + x)) * b))))} is non empty set
{{(- x),(x + (y + (- ((F,S,a,b,(y + x)) * b))))},{(- x)}} is non empty set
the addF of S . [(- x),(x + (y + (- ((F,S,a,b,(y + x)) * b))))] is set
(- x) + x is Element of the carrier of S
the addF of S . ((- x),x) is Element of the carrier of S
[(- x),x] is set
{(- x),x} is non empty set
{{(- x),x},{(- x)}} is non empty set
the addF of S . [(- x),x] is set
((- x) + x) + (y + (- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
the addF of S . (((- x) + x),(y + (- ((F,S,a,b,(y + x)) * b)))) is Element of the carrier of S
[((- x) + x),(y + (- ((F,S,a,b,(y + x)) * b)))] is set
{((- x) + x),(y + (- ((F,S,a,b,(y + x)) * b)))} is non empty set
{((- x) + x)} is non empty set
{{((- x) + x),(y + (- ((F,S,a,b,(y + x)) * b)))},{((- x) + x)}} is non empty set
the addF of S . [((- x) + x),(y + (- ((F,S,a,b,(y + x)) * b)))] is set
(0. S) + (y + (- ((F,S,a,b,(y + x)) * b))) is Element of the carrier of S
the addF of S . ((0. S),(y + (- ((F,S,a,b,(y + x)) * b)))) is Element of the carrier of S
[(0. S),(y + (- ((F,S,a,b,(y + x)) * b)))] is set
{(0. S),(y + (- ((F,S,a,b,(y + x)) * b)))} is non empty set
{(0. S)} is non empty set
{{(0. S),(y + (- ((F,S,a,b,(y + x)) * b)))},{(0. S)}} is non empty set
the addF of S . [(0. S),(y + (- ((F,S,a,b,(y + x)) * b)))] is set
y - ((F,S,a,b,(y + x)) * b) is Element of the carrier of S
y + (- ((F,S,a,b,(y + x)) * b)) is Element of the carrier of S
y + (- ((F,S,a,(b + x),y) * b)) is Element of the carrier of S
(y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x) is Element of the carrier of S
(y + (- ((F,S,a,(b + x),y) * b))) + (- ((F,S,a,(b + x),y) * x)) is Element of the carrier of S
the addF of S . ((y + (- ((F,S,a,(b + x),y) * b))),(- ((F,S,a,(b + x),y) * x))) is Element of the carrier of S
[(y + (- ((F,S,a,(b + x),y) * b))),(- ((F,S,a,(b + x),y) * x))] is set
{(y + (- ((F,S,a,(b + x),y) * b))),(- ((F,S,a,(b + x),y) * x))} is non empty set
{(y + (- ((F,S,a,(b + x),y) * b)))} is non empty set
{{(y + (- ((F,S,a,(b + x),y) * b))),(- ((F,S,a,(b + x),y) * x))},{(y + (- ((F,S,a,(b + x),y) * b)))}} is non empty set
the addF of S . [(y + (- ((F,S,a,(b + x),y) * b))),(- ((F,S,a,(b + x),y) * x))] is set
((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x) is Element of the carrier of S
the addF of S . (((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)) is Element of the carrier of S
[((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)] is set
{((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)} is non empty set
{((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x))} is non empty set
{{((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)},{((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x))}} is non empty set
the addF of S . [((y + (- ((F,S,a,(b + x),y) * b))) - ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)] is set
(- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x) is Element of the carrier of S
the addF of S . ((- ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)) is Element of the carrier of S
[(- ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)] is set
{(- ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)} is non empty set
{(- ((F,S,a,(b + x),y) * x))} is non empty set
{{(- ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)},{(- ((F,S,a,(b + x),y) * x))}} is non empty set
the addF of S . [(- ((F,S,a,(b + x),y) * x)),((F,S,a,(b + x),y) * x)] is set
(y + (- ((F,S,a,(b + x),y) * b))) + ((- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x)) is Element of the carrier of S
the addF of S . ((y + (- ((F,S,a,(b + x),y) * b))),((- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x))) is Element of the carrier of S
[(y + (- ((F,S,a,(b + x),y) * b))),((- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x))] is set
{(y + (- ((F,S,a,(b + x),y) * b))),((- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x))} is non empty set
{{(y + (- ((F,S,a,(b + x),y) * b))),((- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x))},{(y + (- ((F,S,a,(b + x),y) * b)))}} is non empty set
the addF of S . [(y + (- ((F,S,a,(b + x),y) * b))),((- ((F,S,a,(b + x),y) * x)) + ((F,S,a,(b + x),y) * x))] is set
(y + (- ((F,S,a,(b + x),y) * b))) + (0. S) is Element of the carrier of S
the addF of S . ((y + (- ((F,S,a,(b + x),y) * b))),(0. S)) is Element of the carrier of S
[(y + (- ((F,S,a,(b + x),y) * b))),(0. S)] is set
{(y + (- ((F,S,a,(b + x),y) * b))),(0. S)} is non empty set
{{(y + (- ((F,S,a,(b + x),y) * b))),(0. S)},{(y + (- ((F,S,a,(b + x),y) * b)))}} is non empty set
the addF of S . [(y + (- ((F,S,a,(b + x),y) * b))),(0. S)] is set
(F,S,a,b,y) * b is Element of the carrier of S
y - ((F,S,a,b,y) * b) is Element of the carrier of S
- ((F,S,a,b,y) * b) is Element of the carrier of S
y + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[y,(- ((F,S,a,b,y) * b))] is set
{y,(- ((F,S,a,b,y) * b))} is non empty set
{{y,(- ((F,S,a,b,y) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,b,y) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
a + x is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (a,x) is Element of the carrier of S
[a,x] is set
{a,x} is non empty set
{a} is non empty set
{{a,x},{a}} is non empty set
the addF of S . [a,x] is set
y is Element of the carrier of S
(F,S,(a + x),b,y) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,a,b,y) is Element of the carrier of F
(F,S,a,b,y) * b is Element of the carrier of S
- ((F,S,a,b,y) * b) is Element of the carrier of S
y + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[y,(- ((F,S,a,b,y) * b))] is set
{y,(- ((F,S,a,b,y) * b))} is non empty set
{y} is non empty set
{{y,(- ((F,S,a,b,y) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,b,y) * b))] is set
y - ((F,S,a,b,y) * b) is Element of the carrier of S
y + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
(F,S,(a + x),b,y) * b is Element of the carrier of S
y - ((F,S,(a + x),b,y) * b) is Element of the carrier of S
- ((F,S,(a + x),b,y) * b) is Element of the carrier of S
y + (- ((F,S,(a + x),b,y) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,(a + x),b,y) * b))) is Element of the carrier of S
[y,(- ((F,S,(a + x),b,y) * b))] is set
{y,(- ((F,S,(a + x),b,y) * b))} is non empty set
{{y,(- ((F,S,(a + x),b,y) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,(a + x),b,y) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
x - b is Element of the carrier of S
- b is Element of the carrier of S
x + (- b) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(- b)) is Element of the carrier of S
[x,(- b)] is set
{x,(- b)} is non empty set
{x} is non empty set
{{x,(- b)},{x}} is non empty set
the addF of S . [x,(- b)] is set
(F,S,a,b,x) is Element of the carrier of F
(1_ F) * b is Element of the carrier of S
x - ((1_ F) * b) is Element of the carrier of S
- ((1_ F) * b) is Element of the carrier of S
x + (- ((1_ F) * b)) is Element of the carrier of S
the addF of S . (x,(- ((1_ F) * b))) is Element of the carrier of S
[x,(- ((1_ F) * b))] is set
{x,(- ((1_ F) * b))} is non empty set
{{x,(- ((1_ F) * b))},{x}} is non empty set
the addF of S . [x,(- ((1_ F) * b))] is set
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
1_ F is Element of the carrier of F
the carrier of F is non empty non trivial set
K173(F) is V53(F) Element of the carrier of F
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
(F,S,a,b,b) is Element of the carrier of F
b - b is Element of the carrier of S
- b is Element of the carrier of S
b + (- b) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (b,(- b)) is Element of the carrier of S
[b,(- b)] is set
{b,(- b)} is non empty set
{b} is non empty set
{{b,(- b)},{b}} is non empty set
the addF of S . [b,(- b)] is set
0. S is V53(S) Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
0. F is V53(F) Element of the carrier of F
the carrier of F is non empty non trivial set
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
0. S is V53(S) Element of the carrier of S
x + (0. S) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,(0. S)) is Element of the carrier of S
[x,(0. S)] is set
{x,(0. S)} is non empty set
{x} is non empty set
{{x,(0. S)},{x}} is non empty set
the addF of S . [x,(0. S)] is set
- (0. S) is Element of the carrier of S
x + (- (0. S)) is Element of the carrier of S
the addF of S . (x,(- (0. S))) is Element of the carrier of S
[x,(- (0. S))] is set
{x,(- (0. S))} is non empty set
{{x,(- (0. S))},{x}} is non empty set
the addF of S . [x,(- (0. S))] is set
(0. F) * b is Element of the carrier of S
x - ((0. F) * b) is Element of the carrier of S
- ((0. F) * b) is Element of the carrier of S
x + (- ((0. F) * b)) is Element of the carrier of S
the addF of S . (x,(- ((0. F) * b))) is Element of the carrier of S
[x,(- ((0. F) * b))] is set
{x,(- ((0. F) * b))} is non empty set
{{x,(- ((0. F) * b))},{x}} is non empty set
the addF of S . [x,(- ((0. F) * b))] is set
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,a,b,x) " is Element of the carrier of F
y is Element of the carrier of S
(F,S,a,b,y) is Element of the carrier of F
(F,S,a,b,y) * ((F,S,a,b,x) ") is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,b,y),((F,S,a,b,x) ")) is Element of the carrier of F
[(F,S,a,b,y),((F,S,a,b,x) ")] is set
{(F,S,a,b,y),((F,S,a,b,x) ")} is non empty set
{(F,S,a,b,y)} is non empty set
{{(F,S,a,b,y),((F,S,a,b,x) ")},{(F,S,a,b,y)}} is non empty set
the multF of F . [(F,S,a,b,y),((F,S,a,b,x) ")] is set
(F,S,a,x,y) is Element of the carrier of F
(F,S,a,x,y) * x is Element of the carrier of S
(F,S,a,b,((F,S,a,x,y) * x)) is Element of the carrier of F
(F,S,a,b,((F,S,a,x,y) * x)) * b is Element of the carrier of S
((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b) is Element of the carrier of S
- ((F,S,a,b,((F,S,a,x,y) * x)) * b) is Element of the carrier of S
((F,S,a,x,y) * x) + (- ((F,S,a,b,((F,S,a,x,y) * x)) * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (((F,S,a,x,y) * x),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))) is Element of the carrier of S
[((F,S,a,x,y) * x),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
{((F,S,a,x,y) * x),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))} is non empty set
{((F,S,a,x,y) * x)} is non empty set
{{((F,S,a,x,y) * x),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))},{((F,S,a,x,y) * x)}} is non empty set
the addF of S . [((F,S,a,x,y) * x),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
y - ((F,S,a,x,y) * x) is Element of the carrier of S
- ((F,S,a,x,y) * x) is Element of the carrier of S
y + (- ((F,S,a,x,y) * x)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,x,y) * x))) is Element of the carrier of S
[y,(- ((F,S,a,x,y) * x))] is set
{y,(- ((F,S,a,x,y) * x))} is non empty set
{y} is non empty set
{{y,(- ((F,S,a,x,y) * x))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,x,y) * x))] is set
y + (- ((F,S,a,x,y) * x)) is Element of the carrier of S
(y + (- ((F,S,a,x,y) * x))) + (((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b)) is Element of the carrier of S
the addF of S . ((y + (- ((F,S,a,x,y) * x))),(((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b))) is Element of the carrier of S
[(y + (- ((F,S,a,x,y) * x))),(((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
{(y + (- ((F,S,a,x,y) * x))),(((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b))} is non empty set
{(y + (- ((F,S,a,x,y) * x)))} is non empty set
{{(y + (- ((F,S,a,x,y) * x))),(((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b))},{(y + (- ((F,S,a,x,y) * x)))}} is non empty set
the addF of S . [(y + (- ((F,S,a,x,y) * x))),(((F,S,a,x,y) * x) - ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
(y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x) is Element of the carrier of S
the addF of S . ((y + (- ((F,S,a,x,y) * x))),((F,S,a,x,y) * x)) is Element of the carrier of S
[(y + (- ((F,S,a,x,y) * x))),((F,S,a,x,y) * x)] is set
{(y + (- ((F,S,a,x,y) * x))),((F,S,a,x,y) * x)} is non empty set
{{(y + (- ((F,S,a,x,y) * x))),((F,S,a,x,y) * x)},{(y + (- ((F,S,a,x,y) * x)))}} is non empty set
the addF of S . [(y + (- ((F,S,a,x,y) * x))),((F,S,a,x,y) * x)] is set
((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x)) + (- ((F,S,a,b,((F,S,a,x,y) * x)) * b)) is Element of the carrier of S
the addF of S . (((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))) is Element of the carrier of S
[((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
{((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))} is non empty set
{((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x))} is non empty set
{{((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))},{((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x))}} is non empty set
the addF of S . [((y + (- ((F,S,a,x,y) * x))) + ((F,S,a,x,y) * x)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
(- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x) is Element of the carrier of S
the addF of S . ((- ((F,S,a,x,y) * x)),((F,S,a,x,y) * x)) is Element of the carrier of S
[(- ((F,S,a,x,y) * x)),((F,S,a,x,y) * x)] is set
{(- ((F,S,a,x,y) * x)),((F,S,a,x,y) * x)} is non empty set
{(- ((F,S,a,x,y) * x))} is non empty set
{{(- ((F,S,a,x,y) * x)),((F,S,a,x,y) * x)},{(- ((F,S,a,x,y) * x))}} is non empty set
the addF of S . [(- ((F,S,a,x,y) * x)),((F,S,a,x,y) * x)] is set
y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x)) is Element of the carrier of S
the addF of S . (y,((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))) is Element of the carrier of S
[y,((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))] is set
{y,((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))} is non empty set
{{y,((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))},{y}} is non empty set
the addF of S . [y,((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))] is set
(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))) + (- ((F,S,a,b,((F,S,a,x,y) * x)) * b)) is Element of the carrier of S
the addF of S . ((y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))) is Element of the carrier of S
[(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
{(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))} is non empty set
{(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x)))} is non empty set
{{(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))},{(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x)))}} is non empty set
the addF of S . [(y + ((- ((F,S,a,x,y) * x)) + ((F,S,a,x,y) * x))),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
0. S is V53(S) Element of the carrier of S
y + (0. S) is Element of the carrier of S
the addF of S . (y,(0. S)) is Element of the carrier of S
[y,(0. S)] is set
{y,(0. S)} is non empty set
{{y,(0. S)},{y}} is non empty set
the addF of S . [y,(0. S)] is set
(y + (0. S)) + (- ((F,S,a,b,((F,S,a,x,y) * x)) * b)) is Element of the carrier of S
the addF of S . ((y + (0. S)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))) is Element of the carrier of S
[(y + (0. S)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
{(y + (0. S)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))} is non empty set
{(y + (0. S))} is non empty set
{{(y + (0. S)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))},{(y + (0. S))}} is non empty set
the addF of S . [(y + (0. S)),(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
y - ((F,S,a,b,((F,S,a,x,y) * x)) * b) is Element of the carrier of S
y + (- ((F,S,a,b,((F,S,a,x,y) * x)) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))) is Element of the carrier of S
[y,(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
{y,(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))} is non empty set
{{y,(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,b,((F,S,a,x,y) * x)) * b))] is set
(F,S,a,x,y) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . ((F,S,a,x,y),(F,S,a,b,x)) is Element of the carrier of F
[(F,S,a,x,y),(F,S,a,b,x)] is set
{(F,S,a,x,y),(F,S,a,b,x)} is non empty set
{(F,S,a,x,y)} is non empty set
{{(F,S,a,x,y),(F,S,a,b,x)},{(F,S,a,x,y)}} is non empty set
the multF of F . [(F,S,a,x,y),(F,S,a,b,x)] is set
((F,S,a,x,y) * (F,S,a,b,x)) * b is Element of the carrier of S
y - (((F,S,a,x,y) * (F,S,a,b,x)) * b) is Element of the carrier of S
- (((F,S,a,x,y) * (F,S,a,b,x)) * b) is Element of the carrier of S
y + (- (((F,S,a,x,y) * (F,S,a,b,x)) * b)) is Element of the carrier of S
the addF of S . (y,(- (((F,S,a,x,y) * (F,S,a,b,x)) * b))) is Element of the carrier of S
[y,(- (((F,S,a,x,y) * (F,S,a,b,x)) * b))] is set
{y,(- (((F,S,a,x,y) * (F,S,a,b,x)) * b))} is non empty set
{{y,(- (((F,S,a,x,y) * (F,S,a,b,x)) * b))},{y}} is non empty set
the addF of S . [y,(- (((F,S,a,x,y) * (F,S,a,b,x)) * b))] is set
(F,S,a,b,y) * b is Element of the carrier of S
y - ((F,S,a,b,y) * b) is Element of the carrier of S
- ((F,S,a,b,y) * b) is Element of the carrier of S
y + (- ((F,S,a,b,y) * b)) is Element of the carrier of S
the addF of S . (y,(- ((F,S,a,b,y) * b))) is Element of the carrier of S
[y,(- ((F,S,a,b,y) * b))] is set
{y,(- ((F,S,a,b,y) * b))} is non empty set
{{y,(- ((F,S,a,b,y) * b))},{y}} is non empty set
the addF of S . [y,(- ((F,S,a,b,y) * b))] is set
(F,S,a,b,x) * ((F,S,a,b,x) ") is Element of the carrier of F
the multF of F . ((F,S,a,b,x),((F,S,a,b,x) ")) is Element of the carrier of F
[(F,S,a,b,x),((F,S,a,b,x) ")] is set
{(F,S,a,b,x),((F,S,a,b,x) ")} is non empty set
{(F,S,a,b,x)} is non empty set
{{(F,S,a,b,x),((F,S,a,b,x) ")},{(F,S,a,b,x)}} is non empty set
the multF of F . [(F,S,a,b,x),((F,S,a,b,x) ")] is set
(F,S,a,x,y) * ((F,S,a,b,x) * ((F,S,a,b,x) ")) is Element of the carrier of F
the multF of F . ((F,S,a,x,y),((F,S,a,b,x) * ((F,S,a,b,x) "))) is Element of the carrier of F
[(F,S,a,x,y),((F,S,a,b,x) * ((F,S,a,b,x) "))] is set
{(F,S,a,x,y),((F,S,a,b,x) * ((F,S,a,b,x) "))} is non empty set
{{(F,S,a,x,y),((F,S,a,b,x) * ((F,S,a,b,x) "))},{(F,S,a,x,y)}} is non empty set
the multF of F . [(F,S,a,x,y),((F,S,a,b,x) * ((F,S,a,b,x) "))] is set
0. F is V53(F) Element of the carrier of F
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(F,S,a,x,y) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,a,x,y),(1_ F)) is Element of the carrier of F
[(F,S,a,x,y),(1_ F)] is set
{(F,S,a,x,y),(1_ F)} is non empty set
{{(F,S,a,x,y),(1_ F)},{(F,S,a,x,y)}} is non empty set
the multF of F . [(F,S,a,x,y),(1_ F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,a,x,b) is Element of the carrier of F
(F,S,a,x,b) " is Element of the carrier of F
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
0. F is V53(F) Element of the carrier of F
(F,S,a,b,b) is Element of the carrier of F
(F,S,a,b,x) " is Element of the carrier of F
(F,S,a,b,b) * ((F,S,a,b,x) ") is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,b,b),((F,S,a,b,x) ")) is Element of the carrier of F
[(F,S,a,b,b),((F,S,a,b,x) ")] is set
{(F,S,a,b,b),((F,S,a,b,x) ")} is non empty set
{(F,S,a,b,b)} is non empty set
{{(F,S,a,b,b),((F,S,a,b,x) ")},{(F,S,a,b,b)}} is non empty set
the multF of F . [(F,S,a,b,b),((F,S,a,b,x) ")] is set
((F,S,a,b,x) ") * (1_ F) is Element of the carrier of F
the multF of F . (((F,S,a,b,x) "),(1_ F)) is Element of the carrier of F
[((F,S,a,b,x) "),(1_ F)] is set
{((F,S,a,b,x) "),(1_ F)} is non empty set
{((F,S,a,b,x) ")} is non empty set
{{((F,S,a,b,x) "),(1_ F)},{((F,S,a,b,x) ")}} is non empty set
the multF of F . [((F,S,a,b,x) "),(1_ F)] is set
(F,S,a,x,b) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . ((F,S,a,x,b),(F,S,a,b,x)) is Element of the carrier of F
[(F,S,a,x,b),(F,S,a,b,x)] is set
{(F,S,a,x,b),(F,S,a,b,x)} is non empty set
{(F,S,a,x,b)} is non empty set
{{(F,S,a,x,b),(F,S,a,b,x)},{(F,S,a,x,b)}} is non empty set
the multF of F . [(F,S,a,x,b),(F,S,a,b,x)] is set
((F,S,a,x,b) ") * ((F,S,a,x,b) * (F,S,a,b,x)) is Element of the carrier of F
the multF of F . (((F,S,a,x,b) "),((F,S,a,x,b) * (F,S,a,b,x))) is Element of the carrier of F
[((F,S,a,x,b) "),((F,S,a,x,b) * (F,S,a,b,x))] is set
{((F,S,a,x,b) "),((F,S,a,x,b) * (F,S,a,b,x))} is non empty set
{((F,S,a,x,b) ")} is non empty set
{{((F,S,a,x,b) "),((F,S,a,x,b) * (F,S,a,b,x))},{((F,S,a,x,b) ")}} is non empty set
the multF of F . [((F,S,a,x,b) "),((F,S,a,x,b) * (F,S,a,b,x))] is set
((F,S,a,x,b) ") * (F,S,a,x,b) is Element of the carrier of F
the multF of F . (((F,S,a,x,b) "),(F,S,a,x,b)) is Element of the carrier of F
[((F,S,a,x,b) "),(F,S,a,x,b)] is set
{((F,S,a,x,b) "),(F,S,a,x,b)} is non empty set
{{((F,S,a,x,b) "),(F,S,a,x,b)},{((F,S,a,x,b) ")}} is non empty set
the multF of F . [((F,S,a,x,b) "),(F,S,a,x,b)] is set
(((F,S,a,x,b) ") * (F,S,a,x,b)) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . ((((F,S,a,x,b) ") * (F,S,a,x,b)),(F,S,a,b,x)) is Element of the carrier of F
[(((F,S,a,x,b) ") * (F,S,a,x,b)),(F,S,a,b,x)] is set
{(((F,S,a,x,b) ") * (F,S,a,x,b)),(F,S,a,b,x)} is non empty set
{(((F,S,a,x,b) ") * (F,S,a,x,b))} is non empty set
{{(((F,S,a,x,b) ") * (F,S,a,x,b)),(F,S,a,b,x)},{(((F,S,a,x,b) ") * (F,S,a,x,b))}} is non empty set
the multF of F . [(((F,S,a,x,b) ") * (F,S,a,x,b)),(F,S,a,b,x)] is set
(F,S,a,b,x) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,a,b,x),(1_ F)) is Element of the carrier of F
[(F,S,a,b,x),(1_ F)] is set
{(F,S,a,b,x),(1_ F)} is non empty set
{(F,S,a,b,x)} is non empty set
{{(F,S,a,b,x),(1_ F)},{(F,S,a,b,x)}} is non empty set
the multF of F . [(F,S,a,b,x),(1_ F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
x + a is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (x,a) is Element of the carrier of S
[x,a] is set
{x,a} is non empty set
{x} is non empty set
{{x,a},{x}} is non empty set
the addF of S . [x,a] is set
(F,S,a,b,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,x,b,a) is Element of the carrier of F
- (F,S,x,b,a) is Element of the carrier of F
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(F,S,a,b,x) * b is Element of the carrier of S
x - ((F,S,a,b,x) * b) is Element of the carrier of S
- ((F,S,a,b,x) * b) is Element of the carrier of S
x + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . (x,(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[x,(- ((F,S,a,b,x) * b))] is set
{x,(- ((F,S,a,b,x) * b))} is non empty set
{{x,(- ((F,S,a,b,x) * b))},{x}} is non empty set
the addF of S . [x,(- ((F,S,a,b,x) * b))] is set
- (F,S,a,b,x) is Element of the carrier of F
(- (F,S,a,b,x)) * b is Element of the carrier of S
((- (F,S,a,b,x)) * b) + x is Element of the carrier of S
the addF of S . (((- (F,S,a,b,x)) * b),x) is Element of the carrier of S
[((- (F,S,a,b,x)) * b),x] is set
{((- (F,S,a,b,x)) * b),x} is non empty set
{((- (F,S,a,b,x)) * b)} is non empty set
{{((- (F,S,a,b,x)) * b),x},{((- (F,S,a,b,x)) * b)}} is non empty set
the addF of S . [((- (F,S,a,b,x)) * b),x] is set
- (1_ F) is Element of the carrier of F
(- (1_ F)) * (((- (F,S,a,b,x)) * b) + x) is Element of the carrier of S
(- (1_ F)) * ((- (F,S,a,b,x)) * b) is Element of the carrier of S
(- (1_ F)) * x is Element of the carrier of S
((- (1_ F)) * ((- (F,S,a,b,x)) * b)) + ((- (1_ F)) * x) is Element of the carrier of S
the addF of S . (((- (1_ F)) * ((- (F,S,a,b,x)) * b)),((- (1_ F)) * x)) is Element of the carrier of S
[((- (1_ F)) * ((- (F,S,a,b,x)) * b)),((- (1_ F)) * x)] is set
{((- (1_ F)) * ((- (F,S,a,b,x)) * b)),((- (1_ F)) * x)} is non empty set
{((- (1_ F)) * ((- (F,S,a,b,x)) * b))} is non empty set
{{((- (1_ F)) * ((- (F,S,a,b,x)) * b)),((- (1_ F)) * x)},{((- (1_ F)) * ((- (F,S,a,b,x)) * b))}} is non empty set
the addF of S . [((- (1_ F)) * ((- (F,S,a,b,x)) * b)),((- (1_ F)) * x)] is set
(- (1_ F)) * (- (F,S,a,b,x)) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((- (1_ F)),(- (F,S,a,b,x))) is Element of the carrier of F
[(- (1_ F)),(- (F,S,a,b,x))] is set
{(- (1_ F)),(- (F,S,a,b,x))} is non empty set
{(- (1_ F))} is non empty set
{{(- (1_ F)),(- (F,S,a,b,x))},{(- (1_ F))}} is non empty set
the multF of F . [(- (1_ F)),(- (F,S,a,b,x))] is set
((- (1_ F)) * (- (F,S,a,b,x))) * b is Element of the carrier of S
(((- (1_ F)) * (- (F,S,a,b,x))) * b) + ((- (1_ F)) * x) is Element of the carrier of S
the addF of S . ((((- (1_ F)) * (- (F,S,a,b,x))) * b),((- (1_ F)) * x)) is Element of the carrier of S
[(((- (1_ F)) * (- (F,S,a,b,x))) * b),((- (1_ F)) * x)] is set
{(((- (1_ F)) * (- (F,S,a,b,x))) * b),((- (1_ F)) * x)} is non empty set
{(((- (1_ F)) * (- (F,S,a,b,x))) * b)} is non empty set
{{(((- (1_ F)) * (- (F,S,a,b,x))) * b),((- (1_ F)) * x)},{(((- (1_ F)) * (- (F,S,a,b,x))) * b)}} is non empty set
the addF of S . [(((- (1_ F)) * (- (F,S,a,b,x))) * b),((- (1_ F)) * x)] is set
(F,S,a,b,x) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,a,b,x),(1_ F)) is Element of the carrier of F
[(F,S,a,b,x),(1_ F)] is set
{(F,S,a,b,x),(1_ F)} is non empty set
{(F,S,a,b,x)} is non empty set
{{(F,S,a,b,x),(1_ F)},{(F,S,a,b,x)}} is non empty set
the multF of F . [(F,S,a,b,x),(1_ F)] is set
((F,S,a,b,x) * (1_ F)) * b is Element of the carrier of S
(((F,S,a,b,x) * (1_ F)) * b) + ((- (1_ F)) * x) is Element of the carrier of S
the addF of S . ((((F,S,a,b,x) * (1_ F)) * b),((- (1_ F)) * x)) is Element of the carrier of S
[(((F,S,a,b,x) * (1_ F)) * b),((- (1_ F)) * x)] is set
{(((F,S,a,b,x) * (1_ F)) * b),((- (1_ F)) * x)} is non empty set
{(((F,S,a,b,x) * (1_ F)) * b)} is non empty set
{{(((F,S,a,b,x) * (1_ F)) * b),((- (1_ F)) * x)},{(((F,S,a,b,x) * (1_ F)) * b)}} is non empty set
the addF of S . [(((F,S,a,b,x) * (1_ F)) * b),((- (1_ F)) * x)] is set
((F,S,a,b,x) * b) + ((- (1_ F)) * x) is Element of the carrier of S
the addF of S . (((F,S,a,b,x) * b),((- (1_ F)) * x)) is Element of the carrier of S
[((F,S,a,b,x) * b),((- (1_ F)) * x)] is set
{((F,S,a,b,x) * b),((- (1_ F)) * x)} is non empty set
{((F,S,a,b,x) * b)} is non empty set
{{((F,S,a,b,x) * b),((- (1_ F)) * x)},{((F,S,a,b,x) * b)}} is non empty set
the addF of S . [((F,S,a,b,x) * b),((- (1_ F)) * x)] is set
((F,S,a,b,x) * b) - x is Element of the carrier of S
- x is Element of the carrier of S
((F,S,a,b,x) * b) + (- x) is Element of the carrier of S
the addF of S . (((F,S,a,b,x) * b),(- x)) is Element of the carrier of S
[((F,S,a,b,x) * b),(- x)] is set
{((F,S,a,b,x) * b),(- x)} is non empty set
{{((F,S,a,b,x) * b),(- x)},{((F,S,a,b,x) * b)}} is non empty set
the addF of S . [((F,S,a,b,x) * b),(- x)] is set
- a is Element of the carrier of S
x - (- a) is Element of the carrier of S
- (- a) is Element of the carrier of S
x + (- (- a)) is Element of the carrier of S
the addF of S . (x,(- (- a))) is Element of the carrier of S
[x,(- (- a))] is set
{x,(- (- a))} is non empty set
{{x,(- (- a))},{x}} is non empty set
the addF of S . [x,(- (- a))] is set
(- a) - ((F,S,a,b,x) * b) is Element of the carrier of S
(- a) + (- ((F,S,a,b,x) * b)) is Element of the carrier of S
the addF of S . ((- a),(- ((F,S,a,b,x) * b))) is Element of the carrier of S
[(- a),(- ((F,S,a,b,x) * b))] is set
{(- a),(- ((F,S,a,b,x) * b))} is non empty set
{(- a)} is non empty set
{{(- a),(- ((F,S,a,b,x) * b))},{(- a)}} is non empty set
the addF of S . [(- a),(- ((F,S,a,b,x) * b))] is set
(F,S,x,b,(- a)) is Element of the carrier of F
(F,S,x,b,(- a)) * b is Element of the carrier of S
(- a) - ((F,S,x,b,(- a)) * b) is Element of the carrier of S
- ((F,S,x,b,(- a)) * b) is Element of the carrier of S
(- a) + (- ((F,S,x,b,(- a)) * b)) is Element of the carrier of S
the addF of S . ((- a),(- ((F,S,x,b,(- a)) * b))) is Element of the carrier of S
[(- a),(- ((F,S,x,b,(- a)) * b))] is set
{(- a),(- ((F,S,x,b,(- a)) * b))} is non empty set
{{(- a),(- ((F,S,x,b,(- a)) * b))},{(- a)}} is non empty set
the addF of S . [(- a),(- ((F,S,x,b,(- a)) * b))] is set
(- (1_ F)) * a is Element of the carrier of S
(F,S,x,b,((- (1_ F)) * a)) is Element of the carrier of F
(- (1_ F)) * (F,S,x,b,a) is Element of the carrier of F
the multF of F . ((- (1_ F)),(F,S,x,b,a)) is Element of the carrier of F
[(- (1_ F)),(F,S,x,b,a)] is set
{(- (1_ F)),(F,S,x,b,a)} is non empty set
{{(- (1_ F)),(F,S,x,b,a)},{(- (1_ F))}} is non empty set
the multF of F . [(- (1_ F)),(F,S,x,b,a)] is set
(F,S,x,b,a) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,x,b,a),(1_ F)) is Element of the carrier of F
[(F,S,x,b,a),(1_ F)] is set
{(F,S,x,b,a),(1_ F)} is non empty set
{(F,S,x,b,a)} is non empty set
{{(F,S,x,b,a),(1_ F)},{(F,S,x,b,a)}} is non empty set
the multF of F . [(F,S,x,b,a),(1_ F)] is set
- ((F,S,x,b,a) * (1_ F)) is Element of the carrier of F
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,x,a,b) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,a,b,x) is Element of the carrier of F
(F,S,a,b,x) " is Element of the carrier of F
(F,S,b,a,x) is Element of the carrier of F
((F,S,a,b,x) ") * (F,S,b,a,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . (((F,S,a,b,x) "),(F,S,b,a,x)) is Element of the carrier of F
[((F,S,a,b,x) "),(F,S,b,a,x)] is set
{((F,S,a,b,x) "),(F,S,b,a,x)} is non empty set
{((F,S,a,b,x) ")} is non empty set
{{((F,S,a,b,x) "),(F,S,b,a,x)},{((F,S,a,b,x) ")}} is non empty set
the multF of F . [((F,S,a,b,x) "),(F,S,b,a,x)] is set
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
0. F is V53(F) Element of the carrier of F
- ((F,S,a,b,x) ") is Element of the carrier of F
- (1_ F) is Element of the carrier of F
((F,S,a,b,x) ") * (F,S,a,b,x) is Element of the carrier of F
the multF of F . (((F,S,a,b,x) "),(F,S,a,b,x)) is Element of the carrier of F
[((F,S,a,b,x) "),(F,S,a,b,x)] is set
{((F,S,a,b,x) "),(F,S,a,b,x)} is non empty set
{{((F,S,a,b,x) "),(F,S,a,b,x)},{((F,S,a,b,x) ")}} is non empty set
the multF of F . [((F,S,a,b,x) "),(F,S,a,b,x)] is set
(- (1_ F)) * (((F,S,a,b,x) ") * (F,S,a,b,x)) is Element of the carrier of F
the multF of F . ((- (1_ F)),(((F,S,a,b,x) ") * (F,S,a,b,x))) is Element of the carrier of F
[(- (1_ F)),(((F,S,a,b,x) ") * (F,S,a,b,x))] is set
{(- (1_ F)),(((F,S,a,b,x) ") * (F,S,a,b,x))} is non empty set
{(- (1_ F))} is non empty set
{{(- (1_ F)),(((F,S,a,b,x) ") * (F,S,a,b,x))},{(- (1_ F))}} is non empty set
the multF of F . [(- (1_ F)),(((F,S,a,b,x) ") * (F,S,a,b,x))] is set
(- (1_ F)) * (1_ F) is Element of the carrier of F
the multF of F . ((- (1_ F)),(1_ F)) is Element of the carrier of F
[(- (1_ F)),(1_ F)] is set
{(- (1_ F)),(1_ F)} is non empty set
{{(- (1_ F)),(1_ F)},{(- (1_ F))}} is non empty set
the multF of F . [(- (1_ F)),(1_ F)] is set
(- (1_ F)) * ((F,S,a,b,x) ") is Element of the carrier of F
the multF of F . ((- (1_ F)),((F,S,a,b,x) ")) is Element of the carrier of F
[(- (1_ F)),((F,S,a,b,x) ")] is set
{(- (1_ F)),((F,S,a,b,x) ")} is non empty set
{{(- (1_ F)),((F,S,a,b,x) ")},{(- (1_ F))}} is non empty set
the multF of F . [(- (1_ F)),((F,S,a,b,x) ")] is set
((- (1_ F)) * ((F,S,a,b,x) ")) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . (((- (1_ F)) * ((F,S,a,b,x) ")),(F,S,a,b,x)) is Element of the carrier of F
[((- (1_ F)) * ((F,S,a,b,x) ")),(F,S,a,b,x)] is set
{((- (1_ F)) * ((F,S,a,b,x) ")),(F,S,a,b,x)} is non empty set
{((- (1_ F)) * ((F,S,a,b,x) "))} is non empty set
{{((- (1_ F)) * ((F,S,a,b,x) ")),(F,S,a,b,x)},{((- (1_ F)) * ((F,S,a,b,x) "))}} is non empty set
the multF of F . [((- (1_ F)) * ((F,S,a,b,x) ")),(F,S,a,b,x)] is set
((F,S,a,b,x) ") * (1_ F) is Element of the carrier of F
the multF of F . (((F,S,a,b,x) "),(1_ F)) is Element of the carrier of F
[((F,S,a,b,x) "),(1_ F)] is set
{((F,S,a,b,x) "),(1_ F)} is non empty set
{{((F,S,a,b,x) "),(1_ F)},{((F,S,a,b,x) ")}} is non empty set
the multF of F . [((F,S,a,b,x) "),(1_ F)] is set
- (((F,S,a,b,x) ") * (1_ F)) is Element of the carrier of F
(- (((F,S,a,b,x) ") * (1_ F))) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . ((- (((F,S,a,b,x) ") * (1_ F))),(F,S,a,b,x)) is Element of the carrier of F
[(- (((F,S,a,b,x) ") * (1_ F))),(F,S,a,b,x)] is set
{(- (((F,S,a,b,x) ") * (1_ F))),(F,S,a,b,x)} is non empty set
{(- (((F,S,a,b,x) ") * (1_ F)))} is non empty set
{{(- (((F,S,a,b,x) ") * (1_ F))),(F,S,a,b,x)},{(- (((F,S,a,b,x) ") * (1_ F)))}} is non empty set
the multF of F . [(- (((F,S,a,b,x) ") * (1_ F))),(F,S,a,b,x)] is set
(- ((F,S,a,b,x) ")) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . ((- ((F,S,a,b,x) ")),(F,S,a,b,x)) is Element of the carrier of F
[(- ((F,S,a,b,x) ")),(F,S,a,b,x)] is set
{(- ((F,S,a,b,x) ")),(F,S,a,b,x)} is non empty set
{(- ((F,S,a,b,x) "))} is non empty set
{{(- ((F,S,a,b,x) ")),(F,S,a,b,x)},{(- ((F,S,a,b,x) "))}} is non empty set
the multF of F . [(- ((F,S,a,b,x) ")),(F,S,a,b,x)] is set
(- ((F,S,a,b,x) ")) * x is Element of the carrier of S
(F,S,a,b,((- ((F,S,a,b,x) ")) * x)) is Element of the carrier of F
(- (1_ F)) * b is Element of the carrier of S
((- ((F,S,a,b,x) ")) * x) - ((- (1_ F)) * b) is Element of the carrier of S
- ((- (1_ F)) * b) is Element of the carrier of S
((- ((F,S,a,b,x) ")) * x) + (- ((- (1_ F)) * b)) is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (((- ((F,S,a,b,x) ")) * x),(- ((- (1_ F)) * b))) is Element of the carrier of S
[((- ((F,S,a,b,x) ")) * x),(- ((- (1_ F)) * b))] is set
{((- ((F,S,a,b,x) ")) * x),(- ((- (1_ F)) * b))} is non empty set
{((- ((F,S,a,b,x) ")) * x)} is non empty set
{{((- ((F,S,a,b,x) ")) * x),(- ((- (1_ F)) * b))},{((- ((F,S,a,b,x) ")) * x)}} is non empty set
the addF of S . [((- ((F,S,a,b,x) ")) * x),(- ((- (1_ F)) * b))] is set
- b is Element of the carrier of S
- (- b) is Element of the carrier of S
((- ((F,S,a,b,x) ")) * x) + (- (- b)) is Element of the carrier of S
the addF of S . (((- ((F,S,a,b,x) ")) * x),(- (- b))) is Element of the carrier of S
[((- ((F,S,a,b,x) ")) * x),(- (- b))] is set
{((- ((F,S,a,b,x) ")) * x),(- (- b))} is non empty set
{{((- ((F,S,a,b,x) ")) * x),(- (- b))},{((- ((F,S,a,b,x) ")) * x)}} is non empty set
the addF of S . [((- ((F,S,a,b,x) ")) * x),(- (- b))] is set
((- ((F,S,a,b,x) ")) * x) + b is Element of the carrier of S
the addF of S . (((- ((F,S,a,b,x) ")) * x),b) is Element of the carrier of S
[((- ((F,S,a,b,x) ")) * x),b] is set
{((- ((F,S,a,b,x) ")) * x),b} is non empty set
{{((- ((F,S,a,b,x) ")) * x),b},{((- ((F,S,a,b,x) ")) * x)}} is non empty set
the addF of S . [((- ((F,S,a,b,x) ")) * x),b] is set
(F,S,b,a,((- ((F,S,a,b,x) ")) * x)) is Element of the carrier of F
(F,S,((- ((F,S,a,b,x) ")) * x),a,b) is Element of the carrier of F
- (F,S,((- ((F,S,a,b,x) ")) * x),a,b) is Element of the carrier of F
- (F,S,x,a,b) is Element of the carrier of F
(- ((F,S,a,b,x) ")) * (F,S,b,a,x) is Element of the carrier of F
the multF of F . ((- ((F,S,a,b,x) ")),(F,S,b,a,x)) is Element of the carrier of F
[(- ((F,S,a,b,x) ")),(F,S,b,a,x)] is set
{(- ((F,S,a,b,x) ")),(F,S,b,a,x)} is non empty set
{{(- ((F,S,a,b,x) ")),(F,S,b,a,x)},{(- ((F,S,a,b,x) "))}} is non empty set
the multF of F . [(- ((F,S,a,b,x) ")),(F,S,b,a,x)] is set
- (((F,S,a,b,x) ") * (F,S,b,a,x)) is Element of the carrier of F
(- (((F,S,a,b,x) ") * (F,S,b,a,x))) * (- (1_ F)) is Element of the carrier of F
the multF of F . ((- (((F,S,a,b,x) ") * (F,S,b,a,x))),(- (1_ F))) is Element of the carrier of F
[(- (((F,S,a,b,x) ") * (F,S,b,a,x))),(- (1_ F))] is set
{(- (((F,S,a,b,x) ") * (F,S,b,a,x))),(- (1_ F))} is non empty set
{(- (((F,S,a,b,x) ") * (F,S,b,a,x)))} is non empty set
{{(- (((F,S,a,b,x) ") * (F,S,b,a,x))),(- (1_ F))},{(- (((F,S,a,b,x) ") * (F,S,b,a,x)))}} is non empty set
the multF of F . [(- (((F,S,a,b,x) ") * (F,S,b,a,x))),(- (1_ F))] is set
(- (F,S,x,a,b)) * (- (1_ F)) is Element of the carrier of F
the multF of F . ((- (F,S,x,a,b)),(- (1_ F))) is Element of the carrier of F
[(- (F,S,x,a,b)),(- (1_ F))] is set
{(- (F,S,x,a,b)),(- (1_ F))} is non empty set
{(- (F,S,x,a,b))} is non empty set
{{(- (F,S,x,a,b)),(- (1_ F))},{(- (F,S,x,a,b))}} is non empty set
the multF of F . [(- (F,S,x,a,b)),(- (1_ F))] is set
(((F,S,a,b,x) ") * (F,S,b,a,x)) * (1_ F) is Element of the carrier of F
the multF of F . ((((F,S,a,b,x) ") * (F,S,b,a,x)),(1_ F)) is Element of the carrier of F
[(((F,S,a,b,x) ") * (F,S,b,a,x)),(1_ F)] is set
{(((F,S,a,b,x) ") * (F,S,b,a,x)),(1_ F)} is non empty set
{(((F,S,a,b,x) ") * (F,S,b,a,x))} is non empty set
{{(((F,S,a,b,x) ") * (F,S,b,a,x)),(1_ F)},{(((F,S,a,b,x) ") * (F,S,b,a,x))}} is non empty set
the multF of F . [(((F,S,a,b,x) ") * (F,S,b,a,x)),(1_ F)] is set
(F,S,x,a,b) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,x,a,b),(1_ F)) is Element of the carrier of F
[(F,S,x,a,b),(1_ F)] is set
{(F,S,x,a,b),(1_ F)} is non empty set
{(F,S,x,a,b)} is non empty set
{{(F,S,x,a,b),(1_ F)},{(F,S,x,a,b)}} is non empty set
the multF of F . [(F,S,x,a,b),(1_ F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,b,a,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
y is Element of the carrier of S
(F,S,a,y,b) is Element of the carrier of F
(F,S,a,y,b) * (F,S,b,a,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,y,b),(F,S,b,a,x)) is Element of the carrier of F
[(F,S,a,y,b),(F,S,b,a,x)] is set
{(F,S,a,y,b),(F,S,b,a,x)} is non empty set
{(F,S,a,y,b)} is non empty set
{{(F,S,a,y,b),(F,S,b,a,x)},{(F,S,a,y,b)}} is non empty set
the multF of F . [(F,S,a,y,b),(F,S,b,a,x)] is set
(F,S,y,a,x) is Element of the carrier of F
(F,S,x,y,b) is Element of the carrier of F
(F,S,y,a,x) * (F,S,x,y,b) is Element of the carrier of F
the multF of F . ((F,S,y,a,x),(F,S,x,y,b)) is Element of the carrier of F
[(F,S,y,a,x),(F,S,x,y,b)] is set
{(F,S,y,a,x),(F,S,x,y,b)} is non empty set
{(F,S,y,a,x)} is non empty set
{{(F,S,y,a,x),(F,S,x,y,b)},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),(F,S,x,y,b)] is set
0. F is V53(F) Element of the carrier of F
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
0. S is V53(S) Element of the carrier of S
p is Element of the carrier of S
(F,S,p,y,b) is Element of the carrier of F
(F,S,y,a,x) " is Element of the carrier of F
((F,S,a,y,b) * (F,S,b,a,x)) * ((F,S,y,a,x) ") is Element of the carrier of F
the multF of F . (((F,S,a,y,b) * (F,S,b,a,x)),((F,S,y,a,x) ")) is Element of the carrier of F
[((F,S,a,y,b) * (F,S,b,a,x)),((F,S,y,a,x) ")] is set
{((F,S,a,y,b) * (F,S,b,a,x)),((F,S,y,a,x) ")} is non empty set
{((F,S,a,y,b) * (F,S,b,a,x))} is non empty set
{{((F,S,a,y,b) * (F,S,b,a,x)),((F,S,y,a,x) ")},{((F,S,a,y,b) * (F,S,b,a,x))}} is non empty set
the multF of F . [((F,S,a,y,b) * (F,S,b,a,x)),((F,S,y,a,x) ")] is set
(F,S,a,p,b) is Element of the carrier of F
(F,S,a,p,y) is Element of the carrier of F
(F,S,a,p,y) " is Element of the carrier of F
(F,S,a,p,b) * ((F,S,a,p,y) ") is Element of the carrier of F
the multF of F . ((F,S,a,p,b),((F,S,a,p,y) ")) is Element of the carrier of F
[(F,S,a,p,b),((F,S,a,p,y) ")] is set
{(F,S,a,p,b),((F,S,a,p,y) ")} is non empty set
{(F,S,a,p,b)} is non empty set
{{(F,S,a,p,b),((F,S,a,p,y) ")},{(F,S,a,p,b)}} is non empty set
the multF of F . [(F,S,a,p,b),((F,S,a,p,y) ")] is set
((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x) is Element of the carrier of F
the multF of F . (((F,S,a,p,b) * ((F,S,a,p,y) ")),(F,S,b,a,x)) is Element of the carrier of F
[((F,S,a,p,b) * ((F,S,a,p,y) ")),(F,S,b,a,x)] is set
{((F,S,a,p,b) * ((F,S,a,p,y) ")),(F,S,b,a,x)} is non empty set
{((F,S,a,p,b) * ((F,S,a,p,y) "))} is non empty set
{{((F,S,a,p,b) * ((F,S,a,p,y) ")),(F,S,b,a,x)},{((F,S,a,p,b) * ((F,S,a,p,y) "))}} is non empty set
the multF of F . [((F,S,a,p,b) * ((F,S,a,p,y) ")),(F,S,b,a,x)] is set
(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x)) * ((F,S,y,a,x) ") is Element of the carrier of F
the multF of F . ((((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x)),((F,S,y,a,x) ")) is Element of the carrier of F
[(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x)),((F,S,y,a,x) ")] is set
{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x)),((F,S,y,a,x) ")} is non empty set
{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x))} is non empty set
{{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x)),((F,S,y,a,x) ")},{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x))}} is non empty set
the multF of F . [(((F,S,a,p,b) * ((F,S,a,p,y) ")) * (F,S,b,a,x)),((F,S,y,a,x) ")] is set
(F,S,b,p,x) is Element of the carrier of F
(F,S,b,p,a) is Element of the carrier of F
(F,S,b,p,a) " is Element of the carrier of F
(F,S,b,p,x) * ((F,S,b,p,a) ") is Element of the carrier of F
the multF of F . ((F,S,b,p,x),((F,S,b,p,a) ")) is Element of the carrier of F
[(F,S,b,p,x),((F,S,b,p,a) ")] is set
{(F,S,b,p,x),((F,S,b,p,a) ")} is non empty set
{(F,S,b,p,x)} is non empty set
{{(F,S,b,p,x),((F,S,b,p,a) ")},{(F,S,b,p,x)}} is non empty set
the multF of F . [(F,S,b,p,x),((F,S,b,p,a) ")] is set
((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")) is Element of the carrier of F
the multF of F . (((F,S,a,p,b) * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))) is Element of the carrier of F
[((F,S,a,p,b) * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))] is set
{((F,S,a,p,b) * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))} is non empty set
{{((F,S,a,p,b) * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))},{((F,S,a,p,b) * ((F,S,a,p,y) "))}} is non empty set
the multF of F . [((F,S,a,p,b) * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))] is set
(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))) * ((F,S,y,a,x) ") is Element of the carrier of F
the multF of F . ((((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,a,x) ")) is Element of the carrier of F
[(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,a,x) ")] is set
{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,a,x) ")} is non empty set
{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")))} is non empty set
{{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,a,x) ")},{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")))}} is non empty set
the multF of F . [(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,a,x) ")] is set
(F,S,y,x,a) is Element of the carrier of F
(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))) * (F,S,y,x,a) is Element of the carrier of F
the multF of F . ((((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),(F,S,y,x,a)) is Element of the carrier of F
[(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),(F,S,y,x,a)] is set
{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),(F,S,y,x,a)} is non empty set
{{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),(F,S,y,x,a)},{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")))}} is non empty set
the multF of F . [(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),(F,S,y,x,a)] is set
(F,S,y,p,a) is Element of the carrier of F
(F,S,y,p,x) is Element of the carrier of F
(F,S,y,p,x) " is Element of the carrier of F
(F,S,y,p,a) * ((F,S,y,p,x) ") is Element of the carrier of F
the multF of F . ((F,S,y,p,a),((F,S,y,p,x) ")) is Element of the carrier of F
[(F,S,y,p,a),((F,S,y,p,x) ")] is set
{(F,S,y,p,a),((F,S,y,p,x) ")} is non empty set
{(F,S,y,p,a)} is non empty set
{{(F,S,y,p,a),((F,S,y,p,x) ")},{(F,S,y,p,a)}} is non empty set
the multF of F . [(F,S,y,p,a),((F,S,y,p,x) ")] is set
(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))) * ((F,S,y,p,a) * ((F,S,y,p,x) ")) is Element of the carrier of F
the multF of F . ((((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))) is Element of the carrier of F
[(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))} is non empty set
{{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))},{(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")))}} is non empty set
the multF of F . [(((F,S,a,p,b) * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
(F,S,a,b,p) is Element of the carrier of F
(F,S,a,b,p) " is Element of the carrier of F
((F,S,a,b,p) ") * ((F,S,a,p,y) ") is Element of the carrier of F
the multF of F . (((F,S,a,b,p) "),((F,S,a,p,y) ")) is Element of the carrier of F
[((F,S,a,b,p) "),((F,S,a,p,y) ")] is set
{((F,S,a,b,p) "),((F,S,a,p,y) ")} is non empty set
{((F,S,a,b,p) ")} is non empty set
{{((F,S,a,b,p) "),((F,S,a,p,y) ")},{((F,S,a,b,p) ")}} is non empty set
the multF of F . [((F,S,a,b,p) "),((F,S,a,p,y) ")] is set
(((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")) is Element of the carrier of F
the multF of F . ((((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))) is Element of the carrier of F
[(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))] is set
{(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))} is non empty set
{(((F,S,a,b,p) ") * ((F,S,a,p,y) "))} is non empty set
{{(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))},{(((F,S,a,b,p) ") * ((F,S,a,p,y) "))}} is non empty set
the multF of F . [(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * ((F,S,b,p,a) "))] is set
((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))) * ((F,S,y,p,a) * ((F,S,y,p,x) ")) is Element of the carrier of F
the multF of F . (((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))) is Element of the carrier of F
[((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))} is non empty set
{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")))} is non empty set
{{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))},{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) ")))}} is non empty set
the multF of F . [((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * ((F,S,b,p,a) "))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
(F,S,b,a,p) is Element of the carrier of F
(F,S,b,p,x) * (F,S,b,a,p) is Element of the carrier of F
the multF of F . ((F,S,b,p,x),(F,S,b,a,p)) is Element of the carrier of F
[(F,S,b,p,x),(F,S,b,a,p)] is set
{(F,S,b,p,x),(F,S,b,a,p)} is non empty set
{{(F,S,b,p,x),(F,S,b,a,p)},{(F,S,b,p,x)}} is non empty set
the multF of F . [(F,S,b,p,x),(F,S,b,a,p)] is set
(((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p)) is Element of the carrier of F
the multF of F . ((((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * (F,S,b,a,p))) is Element of the carrier of F
[(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * (F,S,b,a,p))] is set
{(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * (F,S,b,a,p))} is non empty set
{{(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * (F,S,b,a,p))},{(((F,S,a,b,p) ") * ((F,S,a,p,y) "))}} is non empty set
the multF of F . [(((F,S,a,b,p) ") * ((F,S,a,p,y) ")),((F,S,b,p,x) * (F,S,b,a,p))] is set
((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p))) * ((F,S,y,p,a) * ((F,S,y,p,x) ")) is Element of the carrier of F
the multF of F . (((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))) is Element of the carrier of F
[((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))} is non empty set
{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p)))} is non empty set
{{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))},{((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p)))}} is non empty set
the multF of F . [((((F,S,a,b,p) ") * ((F,S,a,p,y) ")) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
(F,S,a,y,p) is Element of the carrier of F
((F,S,a,b,p) ") * (F,S,a,y,p) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) "),(F,S,a,y,p)) is Element of the carrier of F
[((F,S,a,b,p) "),(F,S,a,y,p)] is set
{((F,S,a,b,p) "),(F,S,a,y,p)} is non empty set
{{((F,S,a,b,p) "),(F,S,a,y,p)},{((F,S,a,b,p) ")}} is non empty set
the multF of F . [((F,S,a,b,p) "),(F,S,a,y,p)] is set
(((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p)) is Element of the carrier of F
the multF of F . ((((F,S,a,b,p) ") * (F,S,a,y,p)),((F,S,b,p,x) * (F,S,b,a,p))) is Element of the carrier of F
[(((F,S,a,b,p) ") * (F,S,a,y,p)),((F,S,b,p,x) * (F,S,b,a,p))] is set
{(((F,S,a,b,p) ") * (F,S,a,y,p)),((F,S,b,p,x) * (F,S,b,a,p))} is non empty set
{(((F,S,a,b,p) ") * (F,S,a,y,p))} is non empty set
{{(((F,S,a,b,p) ") * (F,S,a,y,p)),((F,S,b,p,x) * (F,S,b,a,p))},{(((F,S,a,b,p) ") * (F,S,a,y,p))}} is non empty set
the multF of F . [(((F,S,a,b,p) ") * (F,S,a,y,p)),((F,S,b,p,x) * (F,S,b,a,p))] is set
((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))) * ((F,S,y,p,a) * ((F,S,y,p,x) ")) is Element of the carrier of F
the multF of F . (((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))) is Element of the carrier of F
[((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))} is non empty set
{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p)))} is non empty set
{{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))},{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p)))}} is non empty set
the multF of F . [((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),((F,S,y,p,a) * ((F,S,y,p,x) "))] is set
(F,S,y,a,p) is Element of the carrier of F
(F,S,y,a,p) " is Element of the carrier of F
((F,S,y,a,p) ") * ((F,S,y,p,x) ") is Element of the carrier of F
the multF of F . (((F,S,y,a,p) "),((F,S,y,p,x) ")) is Element of the carrier of F
[((F,S,y,a,p) "),((F,S,y,p,x) ")] is set
{((F,S,y,a,p) "),((F,S,y,p,x) ")} is non empty set
{((F,S,y,a,p) ")} is non empty set
{{((F,S,y,a,p) "),((F,S,y,p,x) ")},{((F,S,y,a,p) ")}} is non empty set
the multF of F . [((F,S,y,a,p) "),((F,S,y,p,x) ")] is set
((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))) * (((F,S,y,a,p) ") * ((F,S,y,p,x) ")) is Element of the carrier of F
the multF of F . (((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))) is Element of the carrier of F
[((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))] is set
{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))} is non empty set
{{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))},{((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p)))}} is non empty set
the multF of F . [((((F,S,a,b,p) ") * (F,S,a,y,p)) * ((F,S,b,p,x) * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))] is set
(F,S,b,x,p) is Element of the carrier of F
(F,S,b,x,p) " is Element of the carrier of F
((F,S,b,x,p) ") * (F,S,b,a,p) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),(F,S,b,a,p)) is Element of the carrier of F
[((F,S,b,x,p) "),(F,S,b,a,p)] is set
{((F,S,b,x,p) "),(F,S,b,a,p)} is non empty set
{((F,S,b,x,p) ")} is non empty set
{{((F,S,b,x,p) "),(F,S,b,a,p)},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),(F,S,b,a,p)] is set
(((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p)) is Element of the carrier of F
the multF of F . ((((F,S,a,b,p) ") * (F,S,a,y,p)),(((F,S,b,x,p) ") * (F,S,b,a,p))) is Element of the carrier of F
[(((F,S,a,b,p) ") * (F,S,a,y,p)),(((F,S,b,x,p) ") * (F,S,b,a,p))] is set
{(((F,S,a,b,p) ") * (F,S,a,y,p)),(((F,S,b,x,p) ") * (F,S,b,a,p))} is non empty set
{{(((F,S,a,b,p) ") * (F,S,a,y,p)),(((F,S,b,x,p) ") * (F,S,b,a,p))},{(((F,S,a,b,p) ") * (F,S,a,y,p))}} is non empty set
the multF of F . [(((F,S,a,b,p) ") * (F,S,a,y,p)),(((F,S,b,x,p) ") * (F,S,b,a,p))] is set
((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p))) * (((F,S,y,a,p) ") * ((F,S,y,p,x) ")) is Element of the carrier of F
the multF of F . (((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))) is Element of the carrier of F
[((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))] is set
{((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))} is non empty set
{((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p)))} is non empty set
{{((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))},{((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p)))}} is non empty set
the multF of F . [((((F,S,a,b,p) ") * (F,S,a,y,p)) * (((F,S,b,x,p) ") * (F,S,b,a,p))),(((F,S,y,a,p) ") * ((F,S,y,p,x) "))] is set
(((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p)) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * (F,S,b,a,p)),(((F,S,a,b,p) ") * (F,S,a,y,p))) is Element of the carrier of F
[(((F,S,b,x,p) ") * (F,S,b,a,p)),(((F,S,a,b,p) ") * (F,S,a,y,p))] is set
{(((F,S,b,x,p) ") * (F,S,b,a,p)),(((F,S,a,b,p) ") * (F,S,a,y,p))} is non empty set
{(((F,S,b,x,p) ") * (F,S,b,a,p))} is non empty set
{{(((F,S,b,x,p) ") * (F,S,b,a,p)),(((F,S,a,b,p) ") * (F,S,a,y,p))},{(((F,S,b,x,p) ") * (F,S,b,a,p))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * (F,S,b,a,p)),(((F,S,a,b,p) ") * (F,S,a,y,p))] is set
(F,S,y,x,p) is Element of the carrier of F
((F,S,y,a,p) ") * (F,S,y,x,p) is Element of the carrier of F
the multF of F . (((F,S,y,a,p) "),(F,S,y,x,p)) is Element of the carrier of F
[((F,S,y,a,p) "),(F,S,y,x,p)] is set
{((F,S,y,a,p) "),(F,S,y,x,p)} is non empty set
{{((F,S,y,a,p) "),(F,S,y,x,p)},{((F,S,y,a,p) ")}} is non empty set
the multF of F . [((F,S,y,a,p) "),(F,S,y,x,p)] is set
((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p))) * (((F,S,y,a,p) ") * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . (((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
[((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
{((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))} is non empty set
{((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p)))} is non empty set
{{((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))},{((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p)))}} is non empty set
the multF of F . [((((F,S,b,x,p) ") * (F,S,b,a,p)) * (((F,S,a,b,p) ") * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
(((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p) is Element of the carrier of F
the multF of F . ((((F,S,a,b,p) ") * (F,S,a,y,p)),(F,S,b,a,p)) is Element of the carrier of F
[(((F,S,a,b,p) ") * (F,S,a,y,p)),(F,S,b,a,p)] is set
{(((F,S,a,b,p) ") * (F,S,a,y,p)),(F,S,b,a,p)} is non empty set
{{(((F,S,a,b,p) ") * (F,S,a,y,p)),(F,S,b,a,p)},{(((F,S,a,b,p) ") * (F,S,a,y,p))}} is non empty set
the multF of F . [(((F,S,a,b,p) ") * (F,S,a,y,p)),(F,S,b,a,p)] is set
((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p)) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))) is Element of the carrier of F
[((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))] is set
{((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))} is non empty set
{{((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))] is set
(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))) * (((F,S,y,a,p) ") * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
[(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))} is non empty set
{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p)))} is non empty set
{{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))},{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p)))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,a,y,p)) * (F,S,b,a,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
((F,S,a,b,p) ") * (F,S,b,a,p) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) "),(F,S,b,a,p)) is Element of the carrier of F
[((F,S,a,b,p) "),(F,S,b,a,p)] is set
{((F,S,a,b,p) "),(F,S,b,a,p)} is non empty set
{{((F,S,a,b,p) "),(F,S,b,a,p)},{((F,S,a,b,p) ")}} is non empty set
the multF of F . [((F,S,a,b,p) "),(F,S,b,a,p)] is set
(((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p) is Element of the carrier of F
the multF of F . ((((F,S,a,b,p) ") * (F,S,b,a,p)),(F,S,a,y,p)) is Element of the carrier of F
[(((F,S,a,b,p) ") * (F,S,b,a,p)),(F,S,a,y,p)] is set
{(((F,S,a,b,p) ") * (F,S,b,a,p)),(F,S,a,y,p)} is non empty set
{(((F,S,a,b,p) ") * (F,S,b,a,p))} is non empty set
{{(((F,S,a,b,p) ") * (F,S,b,a,p)),(F,S,a,y,p)},{(((F,S,a,b,p) ") * (F,S,b,a,p))}} is non empty set
the multF of F . [(((F,S,a,b,p) ") * (F,S,b,a,p)),(F,S,a,y,p)] is set
((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p)) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))) is Element of the carrier of F
[((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))] is set
{((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))} is non empty set
{{((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))] is set
(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))) * (((F,S,y,a,p) ") * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
[(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))} is non empty set
{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p)))} is non empty set
{{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))},{(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p)))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * ((((F,S,a,b,p) ") * (F,S,b,a,p)) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
(F,S,p,a,b) is Element of the carrier of F
(F,S,p,a,b) * (F,S,a,y,p) is Element of the carrier of F
the multF of F . ((F,S,p,a,b),(F,S,a,y,p)) is Element of the carrier of F
[(F,S,p,a,b),(F,S,a,y,p)] is set
{(F,S,p,a,b),(F,S,a,y,p)} is non empty set
{(F,S,p,a,b)} is non empty set
{{(F,S,p,a,b),(F,S,a,y,p)},{(F,S,p,a,b)}} is non empty set
the multF of F . [(F,S,p,a,b),(F,S,a,y,p)] is set
((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p)) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),((F,S,p,a,b) * (F,S,a,y,p))) is Element of the carrier of F
[((F,S,b,x,p) "),((F,S,p,a,b) * (F,S,a,y,p))] is set
{((F,S,b,x,p) "),((F,S,p,a,b) * (F,S,a,y,p))} is non empty set
{{((F,S,b,x,p) "),((F,S,p,a,b) * (F,S,a,y,p))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),((F,S,p,a,b) * (F,S,a,y,p))] is set
(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p))) * (((F,S,y,a,p) ") * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
[(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
{(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))} is non empty set
{(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p)))} is non empty set
{{(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))},{(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p)))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * ((F,S,p,a,b) * (F,S,a,y,p))),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
((F,S,b,x,p) ") * (F,S,p,a,b) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),(F,S,p,a,b)) is Element of the carrier of F
[((F,S,b,x,p) "),(F,S,p,a,b)] is set
{((F,S,b,x,p) "),(F,S,p,a,b)} is non empty set
{{((F,S,b,x,p) "),(F,S,p,a,b)},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),(F,S,p,a,b)] is set
(((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * (F,S,p,a,b)),(F,S,a,y,p)) is Element of the carrier of F
[(((F,S,b,x,p) ") * (F,S,p,a,b)),(F,S,a,y,p)] is set
{(((F,S,b,x,p) ") * (F,S,p,a,b)),(F,S,a,y,p)} is non empty set
{(((F,S,b,x,p) ") * (F,S,p,a,b))} is non empty set
{{(((F,S,b,x,p) ") * (F,S,p,a,b)),(F,S,a,y,p)},{(((F,S,b,x,p) ") * (F,S,p,a,b))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * (F,S,p,a,b)),(F,S,a,y,p)] is set
((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p)) * (((F,S,y,a,p) ") * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . (((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p)),(((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
[((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p)),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
{((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p)),(((F,S,y,a,p) ") * (F,S,y,x,p))} is non empty set
{((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p))} is non empty set
{{((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p)),(((F,S,y,a,p) ") * (F,S,y,x,p))},{((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p))}} is non empty set
the multF of F . [((((F,S,b,x,p) ") * (F,S,p,a,b)) * (F,S,a,y,p)),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
(F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((F,S,a,y,p),(((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
[(F,S,a,y,p),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
{(F,S,a,y,p),(((F,S,y,a,p) ") * (F,S,y,x,p))} is non empty set
{(F,S,a,y,p)} is non empty set
{{(F,S,a,y,p),(((F,S,y,a,p) ") * (F,S,y,x,p))},{(F,S,a,y,p)}} is non empty set
the multF of F . [(F,S,a,y,p),(((F,S,y,a,p) ") * (F,S,y,x,p))] is set
(((F,S,b,x,p) ") * (F,S,p,a,b)) * ((F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p))) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p)))) is Element of the carrier of F
[(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p)))] is set
{(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p)))} is non empty set
{{(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p)))},{(((F,S,b,x,p) ") * (F,S,p,a,b))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,a,y,p) * (((F,S,y,a,p) ") * (F,S,y,x,p)))] is set
((F,S,y,a,p) ") * (F,S,a,y,p) is Element of the carrier of F
the multF of F . (((F,S,y,a,p) "),(F,S,a,y,p)) is Element of the carrier of F
[((F,S,y,a,p) "),(F,S,a,y,p)] is set
{((F,S,y,a,p) "),(F,S,a,y,p)} is non empty set
{{((F,S,y,a,p) "),(F,S,a,y,p)},{((F,S,y,a,p) ")}} is non empty set
the multF of F . [((F,S,y,a,p) "),(F,S,a,y,p)] is set
(((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p) is Element of the carrier of F
the multF of F . ((((F,S,y,a,p) ") * (F,S,a,y,p)),(F,S,y,x,p)) is Element of the carrier of F
[(((F,S,y,a,p) ") * (F,S,a,y,p)),(F,S,y,x,p)] is set
{(((F,S,y,a,p) ") * (F,S,a,y,p)),(F,S,y,x,p)} is non empty set
{(((F,S,y,a,p) ") * (F,S,a,y,p))} is non empty set
{{(((F,S,y,a,p) ") * (F,S,a,y,p)),(F,S,y,x,p)},{(((F,S,y,a,p) ") * (F,S,a,y,p))}} is non empty set
the multF of F . [(((F,S,y,a,p) ") * (F,S,a,y,p)),(F,S,y,x,p)] is set
(((F,S,b,x,p) ") * (F,S,p,a,b)) * ((((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * (F,S,p,a,b)),((((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p))) is Element of the carrier of F
[(((F,S,b,x,p) ") * (F,S,p,a,b)),((((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p))] is set
{(((F,S,b,x,p) ") * (F,S,p,a,b)),((((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p))} is non empty set
{{(((F,S,b,x,p) ") * (F,S,p,a,b)),((((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p))},{(((F,S,b,x,p) ") * (F,S,p,a,b))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * (F,S,p,a,b)),((((F,S,y,a,p) ") * (F,S,a,y,p)) * (F,S,y,x,p))] is set
(F,S,p,y,a) is Element of the carrier of F
(F,S,p,y,a) * (F,S,y,x,p) is Element of the carrier of F
the multF of F . ((F,S,p,y,a),(F,S,y,x,p)) is Element of the carrier of F
[(F,S,p,y,a),(F,S,y,x,p)] is set
{(F,S,p,y,a),(F,S,y,x,p)} is non empty set
{(F,S,p,y,a)} is non empty set
{{(F,S,p,y,a),(F,S,y,x,p)},{(F,S,p,y,a)}} is non empty set
the multF of F . [(F,S,p,y,a),(F,S,y,x,p)] is set
(((F,S,b,x,p) ") * (F,S,p,a,b)) * ((F,S,p,y,a) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,p,y,a) * (F,S,y,x,p))) is Element of the carrier of F
[(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,p,y,a) * (F,S,y,x,p))] is set
{(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,p,y,a) * (F,S,y,x,p))} is non empty set
{{(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,p,y,a) * (F,S,y,x,p))},{(((F,S,b,x,p) ") * (F,S,p,a,b))}} is non empty set
the multF of F . [(((F,S,b,x,p) ") * (F,S,p,a,b)),((F,S,p,y,a) * (F,S,y,x,p))] is set
(F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((F,S,p,a,b),((F,S,p,y,a) * (F,S,y,x,p))) is Element of the carrier of F
[(F,S,p,a,b),((F,S,p,y,a) * (F,S,y,x,p))] is set
{(F,S,p,a,b),((F,S,p,y,a) * (F,S,y,x,p))} is non empty set
{{(F,S,p,a,b),((F,S,p,y,a) * (F,S,y,x,p))},{(F,S,p,a,b)}} is non empty set
the multF of F . [(F,S,p,a,b),((F,S,p,y,a) * (F,S,y,x,p))] is set
((F,S,b,x,p) ") * ((F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p))) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),((F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p)))) is Element of the carrier of F
[((F,S,b,x,p) "),((F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p)))] is set
{((F,S,b,x,p) "),((F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p)))} is non empty set
{{((F,S,b,x,p) "),((F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p)))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),((F,S,p,a,b) * ((F,S,p,y,a) * (F,S,y,x,p)))] is set
(F,S,p,a,b) * (F,S,p,y,a) is Element of the carrier of F
the multF of F . ((F,S,p,a,b),(F,S,p,y,a)) is Element of the carrier of F
[(F,S,p,a,b),(F,S,p,y,a)] is set
{(F,S,p,a,b),(F,S,p,y,a)} is non empty set
{{(F,S,p,a,b),(F,S,p,y,a)},{(F,S,p,a,b)}} is non empty set
the multF of F . [(F,S,p,a,b),(F,S,p,y,a)] is set
((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p) is Element of the carrier of F
the multF of F . (((F,S,p,a,b) * (F,S,p,y,a)),(F,S,y,x,p)) is Element of the carrier of F
[((F,S,p,a,b) * (F,S,p,y,a)),(F,S,y,x,p)] is set
{((F,S,p,a,b) * (F,S,p,y,a)),(F,S,y,x,p)} is non empty set
{((F,S,p,a,b) * (F,S,p,y,a))} is non empty set
{{((F,S,p,a,b) * (F,S,p,y,a)),(F,S,y,x,p)},{((F,S,p,a,b) * (F,S,p,y,a))}} is non empty set
the multF of F . [((F,S,p,a,b) * (F,S,p,y,a)),(F,S,y,x,p)] is set
((F,S,b,x,p) ") * (((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),(((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p))) is Element of the carrier of F
[((F,S,b,x,p) "),(((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p))] is set
{((F,S,b,x,p) "),(((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p))} is non empty set
{{((F,S,b,x,p) "),(((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),(((F,S,p,a,b) * (F,S,p,y,a)) * (F,S,y,x,p))] is set
(F,S,p,a,y) is Element of the carrier of F
(F,S,p,a,y) " is Element of the carrier of F
(F,S,p,a,b) * ((F,S,p,a,y) ") is Element of the carrier of F
the multF of F . ((F,S,p,a,b),((F,S,p,a,y) ")) is Element of the carrier of F
[(F,S,p,a,b),((F,S,p,a,y) ")] is set
{(F,S,p,a,b),((F,S,p,a,y) ")} is non empty set
{{(F,S,p,a,b),((F,S,p,a,y) ")},{(F,S,p,a,b)}} is non empty set
the multF of F . [(F,S,p,a,b),((F,S,p,a,y) ")] is set
((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p) is Element of the carrier of F
the multF of F . (((F,S,p,a,b) * ((F,S,p,a,y) ")),(F,S,y,x,p)) is Element of the carrier of F
[((F,S,p,a,b) * ((F,S,p,a,y) ")),(F,S,y,x,p)] is set
{((F,S,p,a,b) * ((F,S,p,a,y) ")),(F,S,y,x,p)} is non empty set
{((F,S,p,a,b) * ((F,S,p,a,y) "))} is non empty set
{{((F,S,p,a,b) * ((F,S,p,a,y) ")),(F,S,y,x,p)},{((F,S,p,a,b) * ((F,S,p,a,y) "))}} is non empty set
the multF of F . [((F,S,p,a,b) * ((F,S,p,a,y) ")),(F,S,y,x,p)] is set
((F,S,b,x,p) ") * (((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),(((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p))) is Element of the carrier of F
[((F,S,b,x,p) "),(((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p))] is set
{((F,S,b,x,p) "),(((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p))} is non empty set
{{((F,S,b,x,p) "),(((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),(((F,S,p,a,b) * ((F,S,p,a,y) ")) * (F,S,y,x,p))] is set
(F,S,p,y,b) * (F,S,y,x,p) is Element of the carrier of F
the multF of F . ((F,S,p,y,b),(F,S,y,x,p)) is Element of the carrier of F
[(F,S,p,y,b),(F,S,y,x,p)] is set
{(F,S,p,y,b),(F,S,y,x,p)} is non empty set
{(F,S,p,y,b)} is non empty set
{{(F,S,p,y,b),(F,S,y,x,p)},{(F,S,p,y,b)}} is non empty set
the multF of F . [(F,S,p,y,b),(F,S,y,x,p)] is set
((F,S,b,x,p) ") * ((F,S,p,y,b) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . (((F,S,b,x,p) "),((F,S,p,y,b) * (F,S,y,x,p))) is Element of the carrier of F
[((F,S,b,x,p) "),((F,S,p,y,b) * (F,S,y,x,p))] is set
{((F,S,b,x,p) "),((F,S,p,y,b) * (F,S,y,x,p))} is non empty set
{{((F,S,b,x,p) "),((F,S,p,y,b) * (F,S,y,x,p))},{((F,S,b,x,p) ")}} is non empty set
the multF of F . [((F,S,b,x,p) "),((F,S,p,y,b) * (F,S,y,x,p))] is set
(F,S,b,p,x) * ((F,S,p,y,b) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((F,S,b,p,x),((F,S,p,y,b) * (F,S,y,x,p))) is Element of the carrier of F
[(F,S,b,p,x),((F,S,p,y,b) * (F,S,y,x,p))] is set
{(F,S,b,p,x),((F,S,p,y,b) * (F,S,y,x,p))} is non empty set
{{(F,S,b,p,x),((F,S,p,y,b) * (F,S,y,x,p))},{(F,S,b,p,x)}} is non empty set
the multF of F . [(F,S,b,p,x),((F,S,p,y,b) * (F,S,y,x,p))] is set
(F,S,p,x,b) is Element of the carrier of F
(F,S,p,x,b) " is Element of the carrier of F
(F,S,x,p,b) is Element of the carrier of F
((F,S,p,x,b) ") * (F,S,x,p,b) is Element of the carrier of F
the multF of F . (((F,S,p,x,b) "),(F,S,x,p,b)) is Element of the carrier of F
[((F,S,p,x,b) "),(F,S,x,p,b)] is set
{((F,S,p,x,b) "),(F,S,x,p,b)} is non empty set
{((F,S,p,x,b) ")} is non empty set
{{((F,S,p,x,b) "),(F,S,x,p,b)},{((F,S,p,x,b) ")}} is non empty set
the multF of F . [((F,S,p,x,b) "),(F,S,x,p,b)] is set
(((F,S,p,x,b) ") * (F,S,x,p,b)) * ((F,S,p,y,b) * (F,S,y,x,p)) is Element of the carrier of F
the multF of F . ((((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (F,S,y,x,p))) is Element of the carrier of F
[(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (F,S,y,x,p))] is set
{(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (F,S,y,x,p))} is non empty set
{(((F,S,p,x,b) ") * (F,S,x,p,b))} is non empty set
{{(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (F,S,y,x,p))},{(((F,S,p,x,b) ") * (F,S,x,p,b))}} is non empty set
the multF of F . [(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (F,S,y,x,p))] is set
(F,S,x,p,y) is Element of the carrier of F
(F,S,x,p,y) " is Element of the carrier of F
(F,S,p,x,y) is Element of the carrier of F
((F,S,x,p,y) ") * (F,S,p,x,y) is Element of the carrier of F
the multF of F . (((F,S,x,p,y) "),(F,S,p,x,y)) is Element of the carrier of F
[((F,S,x,p,y) "),(F,S,p,x,y)] is set
{((F,S,x,p,y) "),(F,S,p,x,y)} is non empty set
{((F,S,x,p,y) ")} is non empty set
{{((F,S,x,p,y) "),(F,S,p,x,y)},{((F,S,x,p,y) ")}} is non empty set
the multF of F . [((F,S,x,p,y) "),(F,S,p,x,y)] is set
(F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y)) is Element of the carrier of F
the multF of F . ((F,S,p,y,b),(((F,S,x,p,y) ") * (F,S,p,x,y))) is Element of the carrier of F
[(F,S,p,y,b),(((F,S,x,p,y) ") * (F,S,p,x,y))] is set
{(F,S,p,y,b),(((F,S,x,p,y) ") * (F,S,p,x,y))} is non empty set
{{(F,S,p,y,b),(((F,S,x,p,y) ") * (F,S,p,x,y))},{(F,S,p,y,b)}} is non empty set
the multF of F . [(F,S,p,y,b),(((F,S,x,p,y) ") * (F,S,p,x,y))] is set
(((F,S,p,x,b) ") * (F,S,x,p,b)) * ((F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y))) is Element of the carrier of F
the multF of F . ((((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y)))) is Element of the carrier of F
[(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y)))] is set
{(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y)))} is non empty set
{{(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y)))},{(((F,S,p,x,b) ") * (F,S,x,p,b))}} is non empty set
the multF of F . [(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,y,b) * (((F,S,x,p,y) ") * (F,S,p,x,y)))] is set
(F,S,p,y,b) * ((F,S,x,p,y) ") is Element of the carrier of F
the multF of F . ((F,S,p,y,b),((F,S,x,p,y) ")) is Element of the carrier of F
[(F,S,p,y,b),((F,S,x,p,y) ")] is set
{(F,S,p,y,b),((F,S,x,p,y) ")} is non empty set
{{(F,S,p,y,b),((F,S,x,p,y) ")},{(F,S,p,y,b)}} is non empty set
the multF of F . [(F,S,p,y,b),((F,S,x,p,y) ")] is set
(F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . ((F,S,p,x,y),((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
[(F,S,p,x,y),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
{(F,S,p,x,y),((F,S,p,y,b) * ((F,S,x,p,y) "))} is non empty set
{(F,S,p,x,y)} is non empty set
{{(F,S,p,x,y),((F,S,p,y,b) * ((F,S,x,p,y) "))},{(F,S,p,x,y)}} is non empty set
the multF of F . [(F,S,p,x,y),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
(((F,S,p,x,b) ") * (F,S,x,p,b)) * ((F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
the multF of F . ((((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))) is Element of the carrier of F
[(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))] is set
{(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))} is non empty set
{{(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))},{(((F,S,p,x,b) ") * (F,S,x,p,b))}} is non empty set
the multF of F . [(((F,S,p,x,b) ") * (F,S,x,p,b)),((F,S,p,x,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))] is set
(F,S,x,p,b) * ((F,S,p,x,b) ") is Element of the carrier of F
the multF of F . ((F,S,x,p,b),((F,S,p,x,b) ")) is Element of the carrier of F
[(F,S,x,p,b),((F,S,p,x,b) ")] is set
{(F,S,x,p,b),((F,S,p,x,b) ")} is non empty set
{(F,S,x,p,b)} is non empty set
{{(F,S,x,p,b),((F,S,p,x,b) ")},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),((F,S,p,x,b) ")] is set
((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y) is Element of the carrier of F
the multF of F . (((F,S,x,p,b) * ((F,S,p,x,b) ")),(F,S,p,x,y)) is Element of the carrier of F
[((F,S,x,p,b) * ((F,S,p,x,b) ")),(F,S,p,x,y)] is set
{((F,S,x,p,b) * ((F,S,p,x,b) ")),(F,S,p,x,y)} is non empty set
{((F,S,x,p,b) * ((F,S,p,x,b) "))} is non empty set
{{((F,S,x,p,b) * ((F,S,p,x,b) ")),(F,S,p,x,y)},{((F,S,x,p,b) * ((F,S,p,x,b) "))}} is non empty set
the multF of F . [((F,S,x,p,b) * ((F,S,p,x,b) ")),(F,S,p,x,y)] is set
(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y)) * ((F,S,p,y,b) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . ((((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
[(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
{(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))} is non empty set
{(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y))} is non empty set
{{(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))},{(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y))}} is non empty set
the multF of F . [(((F,S,x,p,b) * ((F,S,p,x,b) ")) * (F,S,p,x,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
(F,S,p,x,y) * ((F,S,p,x,b) ") is Element of the carrier of F
the multF of F . ((F,S,p,x,y),((F,S,p,x,b) ")) is Element of the carrier of F
[(F,S,p,x,y),((F,S,p,x,b) ")] is set
{(F,S,p,x,y),((F,S,p,x,b) ")} is non empty set
{{(F,S,p,x,y),((F,S,p,x,b) ")},{(F,S,p,x,y)}} is non empty set
the multF of F . [(F,S,p,x,y),((F,S,p,x,b) ")] is set
(F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) ")) is Element of the carrier of F
the multF of F . ((F,S,x,p,b),((F,S,p,x,y) * ((F,S,p,x,b) "))) is Element of the carrier of F
[(F,S,x,p,b),((F,S,p,x,y) * ((F,S,p,x,b) "))] is set
{(F,S,x,p,b),((F,S,p,x,y) * ((F,S,p,x,b) "))} is non empty set
{{(F,S,x,p,b),((F,S,p,x,y) * ((F,S,p,x,b) "))},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),((F,S,p,x,y) * ((F,S,p,x,b) "))] is set
((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) "))) * ((F,S,p,y,b) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . (((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) "))),((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
[((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) "))),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
{((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) "))),((F,S,p,y,b) * ((F,S,x,p,y) "))} is non empty set
{((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) ")))} is non empty set
{{((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) "))),((F,S,p,y,b) * ((F,S,x,p,y) "))},{((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) ")))}} is non empty set
the multF of F . [((F,S,x,p,b) * ((F,S,p,x,y) * ((F,S,p,x,b) "))),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
(F,S,p,b,y) is Element of the carrier of F
(F,S,x,p,b) * (F,S,p,b,y) is Element of the carrier of F
the multF of F . ((F,S,x,p,b),(F,S,p,b,y)) is Element of the carrier of F
[(F,S,x,p,b),(F,S,p,b,y)] is set
{(F,S,x,p,b),(F,S,p,b,y)} is non empty set
{{(F,S,x,p,b),(F,S,p,b,y)},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),(F,S,p,b,y)] is set
((F,S,x,p,b) * (F,S,p,b,y)) * ((F,S,p,y,b) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . (((F,S,x,p,b) * (F,S,p,b,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
[((F,S,x,p,b) * (F,S,p,b,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
{((F,S,x,p,b) * (F,S,p,b,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))} is non empty set
{((F,S,x,p,b) * (F,S,p,b,y))} is non empty set
{{((F,S,x,p,b) * (F,S,p,b,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))},{((F,S,x,p,b) * (F,S,p,b,y))}} is non empty set
the multF of F . [((F,S,x,p,b) * (F,S,p,b,y)),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
(F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . ((F,S,p,b,y),((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
[(F,S,p,b,y),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
{(F,S,p,b,y),((F,S,p,y,b) * ((F,S,x,p,y) "))} is non empty set
{(F,S,p,b,y)} is non empty set
{{(F,S,p,b,y),((F,S,p,y,b) * ((F,S,x,p,y) "))},{(F,S,p,b,y)}} is non empty set
the multF of F . [(F,S,p,b,y),((F,S,p,y,b) * ((F,S,x,p,y) "))] is set
(F,S,x,p,b) * ((F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) "))) is Element of the carrier of F
the multF of F . ((F,S,x,p,b),((F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))) is Element of the carrier of F
[(F,S,x,p,b),((F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))] is set
{(F,S,x,p,b),((F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))} is non empty set
{{(F,S,x,p,b),((F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),((F,S,p,b,y) * ((F,S,p,y,b) * ((F,S,x,p,y) ")))] is set
(F,S,p,b,y) * (F,S,p,y,b) is Element of the carrier of F
the multF of F . ((F,S,p,b,y),(F,S,p,y,b)) is Element of the carrier of F
[(F,S,p,b,y),(F,S,p,y,b)] is set
{(F,S,p,b,y),(F,S,p,y,b)} is non empty set
{{(F,S,p,b,y),(F,S,p,y,b)},{(F,S,p,b,y)}} is non empty set
the multF of F . [(F,S,p,b,y),(F,S,p,y,b)] is set
((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) ") is Element of the carrier of F
the multF of F . (((F,S,p,b,y) * (F,S,p,y,b)),((F,S,x,p,y) ")) is Element of the carrier of F
[((F,S,p,b,y) * (F,S,p,y,b)),((F,S,x,p,y) ")] is set
{((F,S,p,b,y) * (F,S,p,y,b)),((F,S,x,p,y) ")} is non empty set
{((F,S,p,b,y) * (F,S,p,y,b))} is non empty set
{{((F,S,p,b,y) * (F,S,p,y,b)),((F,S,x,p,y) ")},{((F,S,p,b,y) * (F,S,p,y,b))}} is non empty set
the multF of F . [((F,S,p,b,y) * (F,S,p,y,b)),((F,S,x,p,y) ")] is set
(F,S,x,p,b) * (((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . ((F,S,x,p,b),(((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) "))) is Element of the carrier of F
[(F,S,x,p,b),(((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) "))] is set
{(F,S,x,p,b),(((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) "))} is non empty set
{{(F,S,x,p,b),(((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) "))},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),(((F,S,p,b,y) * (F,S,p,y,b)) * ((F,S,x,p,y) "))] is set
(F,S,p,y,b) " is Element of the carrier of F
((F,S,p,y,b) ") * (F,S,p,y,b) is Element of the carrier of F
the multF of F . (((F,S,p,y,b) "),(F,S,p,y,b)) is Element of the carrier of F
[((F,S,p,y,b) "),(F,S,p,y,b)] is set
{((F,S,p,y,b) "),(F,S,p,y,b)} is non empty set
{((F,S,p,y,b) ")} is non empty set
{{((F,S,p,y,b) "),(F,S,p,y,b)},{((F,S,p,y,b) ")}} is non empty set
the multF of F . [((F,S,p,y,b) "),(F,S,p,y,b)] is set
(((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) ") is Element of the carrier of F
the multF of F . ((((F,S,p,y,b) ") * (F,S,p,y,b)),((F,S,x,p,y) ")) is Element of the carrier of F
[(((F,S,p,y,b) ") * (F,S,p,y,b)),((F,S,x,p,y) ")] is set
{(((F,S,p,y,b) ") * (F,S,p,y,b)),((F,S,x,p,y) ")} is non empty set
{(((F,S,p,y,b) ") * (F,S,p,y,b))} is non empty set
{{(((F,S,p,y,b) ") * (F,S,p,y,b)),((F,S,x,p,y) ")},{(((F,S,p,y,b) ") * (F,S,p,y,b))}} is non empty set
the multF of F . [(((F,S,p,y,b) ") * (F,S,p,y,b)),((F,S,x,p,y) ")] is set
(F,S,x,p,b) * ((((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) ")) is Element of the carrier of F
the multF of F . ((F,S,x,p,b),((((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) "))) is Element of the carrier of F
[(F,S,x,p,b),((((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) "))] is set
{(F,S,x,p,b),((((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) "))} is non empty set
{{(F,S,x,p,b),((((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) "))},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),((((F,S,p,y,b) ") * (F,S,p,y,b)) * ((F,S,x,p,y) "))] is set
((F,S,x,p,y) ") * (1_ F) is Element of the carrier of F
the multF of F . (((F,S,x,p,y) "),(1_ F)) is Element of the carrier of F
[((F,S,x,p,y) "),(1_ F)] is set
{((F,S,x,p,y) "),(1_ F)} is non empty set
{{((F,S,x,p,y) "),(1_ F)},{((F,S,x,p,y) ")}} is non empty set
the multF of F . [((F,S,x,p,y) "),(1_ F)] is set
(F,S,x,p,b) * (((F,S,x,p,y) ") * (1_ F)) is Element of the carrier of F
the multF of F . ((F,S,x,p,b),(((F,S,x,p,y) ") * (1_ F))) is Element of the carrier of F
[(F,S,x,p,b),(((F,S,x,p,y) ") * (1_ F))] is set
{(F,S,x,p,b),(((F,S,x,p,y) ") * (1_ F))} is non empty set
{{(F,S,x,p,b),(((F,S,x,p,y) ") * (1_ F))},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),(((F,S,x,p,y) ") * (1_ F))] is set
(F,S,x,p,b) * ((F,S,x,p,y) ") is Element of the carrier of F
the multF of F . ((F,S,x,p,b),((F,S,x,p,y) ")) is Element of the carrier of F
[(F,S,x,p,b),((F,S,x,p,y) ")] is set
{(F,S,x,p,b),((F,S,x,p,y) ")} is non empty set
{{(F,S,x,p,b),((F,S,x,p,y) ")},{(F,S,x,p,b)}} is non empty set
the multF of F . [(F,S,x,p,b),((F,S,x,p,y) ")] is set
(F,S,y,a,x) * ((F,S,y,a,x) ") is Element of the carrier of F
the multF of F . ((F,S,y,a,x),((F,S,y,a,x) ")) is Element of the carrier of F
[(F,S,y,a,x),((F,S,y,a,x) ")] is set
{(F,S,y,a,x),((F,S,y,a,x) ")} is non empty set
{{(F,S,y,a,x),((F,S,y,a,x) ")},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),((F,S,y,a,x) ")] is set
((F,S,y,a,x) * ((F,S,y,a,x) ")) * ((F,S,a,y,b) * (F,S,b,a,x)) is Element of the carrier of F
the multF of F . (((F,S,y,a,x) * ((F,S,y,a,x) ")),((F,S,a,y,b) * (F,S,b,a,x))) is Element of the carrier of F
[((F,S,y,a,x) * ((F,S,y,a,x) ")),((F,S,a,y,b) * (F,S,b,a,x))] is set
{((F,S,y,a,x) * ((F,S,y,a,x) ")),((F,S,a,y,b) * (F,S,b,a,x))} is non empty set
{((F,S,y,a,x) * ((F,S,y,a,x) "))} is non empty set
{{((F,S,y,a,x) * ((F,S,y,a,x) ")),((F,S,a,y,b) * (F,S,b,a,x))},{((F,S,y,a,x) * ((F,S,y,a,x) "))}} is non empty set
the multF of F . [((F,S,y,a,x) * ((F,S,y,a,x) ")),((F,S,a,y,b) * (F,S,b,a,x))] is set
((F,S,a,y,b) * (F,S,b,a,x)) * (1_ F) is Element of the carrier of F
the multF of F . (((F,S,a,y,b) * (F,S,b,a,x)),(1_ F)) is Element of the carrier of F
[((F,S,a,y,b) * (F,S,b,a,x)),(1_ F)] is set
{((F,S,a,y,b) * (F,S,b,a,x)),(1_ F)} is non empty set
{{((F,S,a,y,b) * (F,S,b,a,x)),(1_ F)},{((F,S,a,y,b) * (F,S,b,a,x))}} is non empty set
the multF of F . [((F,S,a,y,b) * (F,S,b,a,x)),(1_ F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,b,a,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
y is Element of the carrier of S
(F,S,y,a,x) is Element of the carrier of F
z is Element of the carrier of S
(F,S,a,z,b) is Element of the carrier of F
(F,S,a,z,b) * (F,S,b,a,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,z,b),(F,S,b,a,x)) is Element of the carrier of F
[(F,S,a,z,b),(F,S,b,a,x)] is set
{(F,S,a,z,b),(F,S,b,a,x)} is non empty set
{(F,S,a,z,b)} is non empty set
{{(F,S,a,z,b),(F,S,b,a,x)},{(F,S,a,z,b)}} is non empty set
the multF of F . [(F,S,a,z,b),(F,S,b,a,x)] is set
(F,S,a,z,y) is Element of the carrier of F
(F,S,a,z,y) * (F,S,y,a,x) is Element of the carrier of F
the multF of F . ((F,S,a,z,y),(F,S,y,a,x)) is Element of the carrier of F
[(F,S,a,z,y),(F,S,y,a,x)] is set
{(F,S,a,z,y),(F,S,y,a,x)} is non empty set
{(F,S,a,z,y)} is non empty set
{{(F,S,a,z,y),(F,S,y,a,x)},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),(F,S,y,a,x)] is set
0F is Element of the carrier of S
(F,S,x,b,0F) is Element of the carrier of F
((F,S,a,z,b) * (F,S,b,a,x)) * (F,S,x,b,0F) is Element of the carrier of F
the multF of F . (((F,S,a,z,b) * (F,S,b,a,x)),(F,S,x,b,0F)) is Element of the carrier of F
[((F,S,a,z,b) * (F,S,b,a,x)),(F,S,x,b,0F)] is set
{((F,S,a,z,b) * (F,S,b,a,x)),(F,S,x,b,0F)} is non empty set
{((F,S,a,z,b) * (F,S,b,a,x))} is non empty set
{{((F,S,a,z,b) * (F,S,b,a,x)),(F,S,x,b,0F)},{((F,S,a,z,b) * (F,S,b,a,x))}} is non empty set
the multF of F . [((F,S,a,z,b) * (F,S,b,a,x)),(F,S,x,b,0F)] is set
(F,S,x,y,0F) is Element of the carrier of F
((F,S,a,z,y) * (F,S,y,a,x)) * (F,S,x,y,0F) is Element of the carrier of F
the multF of F . (((F,S,a,z,y) * (F,S,y,a,x)),(F,S,x,y,0F)) is Element of the carrier of F
[((F,S,a,z,y) * (F,S,y,a,x)),(F,S,x,y,0F)] is set
{((F,S,a,z,y) * (F,S,y,a,x)),(F,S,x,y,0F)} is non empty set
{((F,S,a,z,y) * (F,S,y,a,x))} is non empty set
{{((F,S,a,z,y) * (F,S,y,a,x)),(F,S,x,y,0F)},{((F,S,a,z,y) * (F,S,y,a,x))}} is non empty set
the multF of F . [((F,S,a,z,y) * (F,S,y,a,x)),(F,S,x,y,0F)] is set
0. F is V53(F) Element of the carrier of F
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(F,S,a,y,b) is Element of the carrier of F
(F,S,a,y,b) * (F,S,b,a,x) is Element of the carrier of F
the multF of F . ((F,S,a,y,b),(F,S,b,a,x)) is Element of the carrier of F
[(F,S,a,y,b),(F,S,b,a,x)] is set
{(F,S,a,y,b),(F,S,b,a,x)} is non empty set
{(F,S,a,y,b)} is non empty set
{{(F,S,a,y,b),(F,S,b,a,x)},{(F,S,a,y,b)}} is non empty set
the multF of F . [(F,S,a,y,b),(F,S,b,a,x)] is set
(F,S,x,y,b) is Element of the carrier of F
(F,S,x,y,b) * (F,S,y,a,x) is Element of the carrier of F
the multF of F . ((F,S,x,y,b),(F,S,y,a,x)) is Element of the carrier of F
[(F,S,x,y,b),(F,S,y,a,x)] is set
{(F,S,x,y,b),(F,S,y,a,x)} is non empty set
{(F,S,x,y,b)} is non empty set
{{(F,S,x,y,b),(F,S,y,a,x)},{(F,S,x,y,b)}} is non empty set
the multF of F . [(F,S,x,y,b),(F,S,y,a,x)] is set
(F,S,a,z,y) " is Element of the carrier of F
(F,S,a,z,b) * ((F,S,a,z,y) ") is Element of the carrier of F
the multF of F . ((F,S,a,z,b),((F,S,a,z,y) ")) is Element of the carrier of F
[(F,S,a,z,b),((F,S,a,z,y) ")] is set
{(F,S,a,z,b),((F,S,a,z,y) ")} is non empty set
{{(F,S,a,z,b),((F,S,a,z,y) ")},{(F,S,a,z,b)}} is non empty set
the multF of F . [(F,S,a,z,b),((F,S,a,z,y) ")] is set
((F,S,a,z,b) * ((F,S,a,z,y) ")) * (F,S,b,a,x) is Element of the carrier of F
the multF of F . (((F,S,a,z,b) * ((F,S,a,z,y) ")),(F,S,b,a,x)) is Element of the carrier of F
[((F,S,a,z,b) * ((F,S,a,z,y) ")),(F,S,b,a,x)] is set
{((F,S,a,z,b) * ((F,S,a,z,y) ")),(F,S,b,a,x)} is non empty set
{((F,S,a,z,b) * ((F,S,a,z,y) "))} is non empty set
{{((F,S,a,z,b) * ((F,S,a,z,y) ")),(F,S,b,a,x)},{((F,S,a,z,b) * ((F,S,a,z,y) "))}} is non empty set
the multF of F . [((F,S,a,z,b) * ((F,S,a,z,y) ")),(F,S,b,a,x)] is set
((F,S,a,z,y) ") * (F,S,a,z,b) is Element of the carrier of F
the multF of F . (((F,S,a,z,y) "),(F,S,a,z,b)) is Element of the carrier of F
[((F,S,a,z,y) "),(F,S,a,z,b)] is set
{((F,S,a,z,y) "),(F,S,a,z,b)} is non empty set
{((F,S,a,z,y) ")} is non empty set
{{((F,S,a,z,y) "),(F,S,a,z,b)},{((F,S,a,z,y) ")}} is non empty set
the multF of F . [((F,S,a,z,y) "),(F,S,a,z,b)] is set
(((F,S,a,z,y) ") * (F,S,a,z,b)) * (F,S,b,a,x) is Element of the carrier of F
the multF of F . ((((F,S,a,z,y) ") * (F,S,a,z,b)),(F,S,b,a,x)) is Element of the carrier of F
[(((F,S,a,z,y) ") * (F,S,a,z,b)),(F,S,b,a,x)] is set
{(((F,S,a,z,y) ") * (F,S,a,z,b)),(F,S,b,a,x)} is non empty set
{(((F,S,a,z,y) ") * (F,S,a,z,b))} is non empty set
{{(((F,S,a,z,y) ") * (F,S,a,z,b)),(F,S,b,a,x)},{(((F,S,a,z,y) ") * (F,S,a,z,b))}} is non empty set
the multF of F . [(((F,S,a,z,y) ") * (F,S,a,z,b)),(F,S,b,a,x)] is set
(F,S,x,0F,b) is Element of the carrier of F
(F,S,x,0F,y) is Element of the carrier of F
(F,S,x,0F,y) " is Element of the carrier of F
(F,S,x,0F,b) * ((F,S,x,0F,y) ") is Element of the carrier of F
the multF of F . ((F,S,x,0F,b),((F,S,x,0F,y) ")) is Element of the carrier of F
[(F,S,x,0F,b),((F,S,x,0F,y) ")] is set
{(F,S,x,0F,b),((F,S,x,0F,y) ")} is non empty set
{(F,S,x,0F,b)} is non empty set
{{(F,S,x,0F,b),((F,S,x,0F,y) ")},{(F,S,x,0F,b)}} is non empty set
the multF of F . [(F,S,x,0F,b),((F,S,x,0F,y) ")] is set
((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x) is Element of the carrier of F
the multF of F . (((F,S,x,0F,b) * ((F,S,x,0F,y) ")),(F,S,y,a,x)) is Element of the carrier of F
[((F,S,x,0F,b) * ((F,S,x,0F,y) ")),(F,S,y,a,x)] is set
{((F,S,x,0F,b) * ((F,S,x,0F,y) ")),(F,S,y,a,x)} is non empty set
{((F,S,x,0F,b) * ((F,S,x,0F,y) "))} is non empty set
{{((F,S,x,0F,b) * ((F,S,x,0F,y) ")),(F,S,y,a,x)},{((F,S,x,0F,b) * ((F,S,x,0F,y) "))}} is non empty set
the multF of F . [((F,S,x,0F,b) * ((F,S,x,0F,y) ")),(F,S,y,a,x)] is set
((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x)) is Element of the carrier of F
the multF of F . (((F,S,a,z,y) "),((F,S,a,z,b) * (F,S,b,a,x))) is Element of the carrier of F
[((F,S,a,z,y) "),((F,S,a,z,b) * (F,S,b,a,x))] is set
{((F,S,a,z,y) "),((F,S,a,z,b) * (F,S,b,a,x))} is non empty set
{{((F,S,a,z,y) "),((F,S,a,z,b) * (F,S,b,a,x))},{((F,S,a,z,y) ")}} is non empty set
the multF of F . [((F,S,a,z,y) "),((F,S,a,z,b) * (F,S,b,a,x))] is set
(F,S,a,z,y) * (((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x))) is Element of the carrier of F
the multF of F . ((F,S,a,z,y),(((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x)))) is Element of the carrier of F
[(F,S,a,z,y),(((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x)))] is set
{(F,S,a,z,y),(((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x)))} is non empty set
{{(F,S,a,z,y),(((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x)))},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),(((F,S,a,z,y) ") * ((F,S,a,z,b) * (F,S,b,a,x)))] is set
(F,S,a,z,y) * (((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x)) is Element of the carrier of F
the multF of F . ((F,S,a,z,y),(((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x))) is Element of the carrier of F
[(F,S,a,z,y),(((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x))] is set
{(F,S,a,z,y),(((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x))} is non empty set
{{(F,S,a,z,y),(((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x))},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),(((F,S,x,0F,b) * ((F,S,x,0F,y) ")) * (F,S,y,a,x))] is set
(F,S,a,z,y) * ((F,S,a,z,y) ") is Element of the carrier of F
the multF of F . ((F,S,a,z,y),((F,S,a,z,y) ")) is Element of the carrier of F
[(F,S,a,z,y),((F,S,a,z,y) ")] is set
{(F,S,a,z,y),((F,S,a,z,y) ")} is non empty set
{{(F,S,a,z,y),((F,S,a,z,y) ")},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),((F,S,a,z,y) ")] is set
((F,S,a,z,y) * ((F,S,a,z,y) ")) * ((F,S,a,z,b) * (F,S,b,a,x)) is Element of the carrier of F
the multF of F . (((F,S,a,z,y) * ((F,S,a,z,y) ")),((F,S,a,z,b) * (F,S,b,a,x))) is Element of the carrier of F
[((F,S,a,z,y) * ((F,S,a,z,y) ")),((F,S,a,z,b) * (F,S,b,a,x))] is set
{((F,S,a,z,y) * ((F,S,a,z,y) ")),((F,S,a,z,b) * (F,S,b,a,x))} is non empty set
{((F,S,a,z,y) * ((F,S,a,z,y) "))} is non empty set
{{((F,S,a,z,y) * ((F,S,a,z,y) ")),((F,S,a,z,b) * (F,S,b,a,x))},{((F,S,a,z,y) * ((F,S,a,z,y) "))}} is non empty set
the multF of F . [((F,S,a,z,y) * ((F,S,a,z,y) ")),((F,S,a,z,b) * (F,S,b,a,x))] is set
((F,S,a,z,b) * (F,S,b,a,x)) * (1_ F) is Element of the carrier of F
the multF of F . (((F,S,a,z,b) * (F,S,b,a,x)),(1_ F)) is Element of the carrier of F
[((F,S,a,z,b) * (F,S,b,a,x)),(1_ F)] is set
{((F,S,a,z,b) * (F,S,b,a,x)),(1_ F)} is non empty set
{{((F,S,a,z,b) * (F,S,b,a,x)),(1_ F)},{((F,S,a,z,b) * (F,S,b,a,x))}} is non empty set
the multF of F . [((F,S,a,z,b) * (F,S,b,a,x)),(1_ F)] is set
(F,S,x,b,0F) " is Element of the carrier of F
((F,S,x,0F,y) ") * ((F,S,x,b,0F) ") is Element of the carrier of F
the multF of F . (((F,S,x,0F,y) "),((F,S,x,b,0F) ")) is Element of the carrier of F
[((F,S,x,0F,y) "),((F,S,x,b,0F) ")] is set
{((F,S,x,0F,y) "),((F,S,x,b,0F) ")} is non empty set
{((F,S,x,0F,y) ")} is non empty set
{{((F,S,x,0F,y) "),((F,S,x,b,0F) ")},{((F,S,x,0F,y) ")}} is non empty set
the multF of F . [((F,S,x,0F,y) "),((F,S,x,b,0F) ")] is set
(((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x) is Element of the carrier of F
the multF of F . ((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")),(F,S,y,a,x)) is Element of the carrier of F
[(((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")),(F,S,y,a,x)] is set
{(((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")),(F,S,y,a,x)} is non empty set
{(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))} is non empty set
{{(((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")),(F,S,y,a,x)},{(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))}} is non empty set
the multF of F . [(((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")),(F,S,y,a,x)] is set
(F,S,a,z,y) * ((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x)) is Element of the carrier of F
the multF of F . ((F,S,a,z,y),((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x))) is Element of the carrier of F
[(F,S,a,z,y),((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x))] is set
{(F,S,a,z,y),((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x))} is non empty set
{{(F,S,a,z,y),((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x))},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),((((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) * (F,S,y,a,x))] is set
(F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")) is Element of the carrier of F
the multF of F . ((F,S,a,z,y),(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))) is Element of the carrier of F
[(F,S,a,z,y),(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))] is set
{(F,S,a,z,y),(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))} is non empty set
{{(F,S,a,z,y),(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),(((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))] is set
((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))) * (F,S,y,a,x) is Element of the carrier of F
the multF of F . (((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))),(F,S,y,a,x)) is Element of the carrier of F
[((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))),(F,S,y,a,x)] is set
{((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))),(F,S,y,a,x)} is non empty set
{((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")))} is non empty set
{{((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))),(F,S,y,a,x)},{((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) ")))}} is non empty set
the multF of F . [((F,S,a,z,y) * (((F,S,x,0F,y) ") * ((F,S,x,b,0F) "))),(F,S,y,a,x)] is set
(F,S,a,z,y) * ((F,S,x,0F,y) ") is Element of the carrier of F
the multF of F . ((F,S,a,z,y),((F,S,x,0F,y) ")) is Element of the carrier of F
[(F,S,a,z,y),((F,S,x,0F,y) ")] is set
{(F,S,a,z,y),((F,S,x,0F,y) ")} is non empty set
{{(F,S,a,z,y),((F,S,x,0F,y) ")},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),((F,S,x,0F,y) ")] is set
((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) ") is Element of the carrier of F
the multF of F . (((F,S,a,z,y) * ((F,S,x,0F,y) ")),((F,S,x,b,0F) ")) is Element of the carrier of F
[((F,S,a,z,y) * ((F,S,x,0F,y) ")),((F,S,x,b,0F) ")] is set
{((F,S,a,z,y) * ((F,S,x,0F,y) ")),((F,S,x,b,0F) ")} is non empty set
{((F,S,a,z,y) * ((F,S,x,0F,y) "))} is non empty set
{{((F,S,a,z,y) * ((F,S,x,0F,y) ")),((F,S,x,b,0F) ")},{((F,S,a,z,y) * ((F,S,x,0F,y) "))}} is non empty set
the multF of F . [((F,S,a,z,y) * ((F,S,x,0F,y) ")),((F,S,x,b,0F) ")] is set
(F,S,y,a,x) * (((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) ")) is Element of the carrier of F
the multF of F . ((F,S,y,a,x),(((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) "))) is Element of the carrier of F
[(F,S,y,a,x),(((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) "))] is set
{(F,S,y,a,x),(((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) "))} is non empty set
{(F,S,y,a,x)} is non empty set
{{(F,S,y,a,x),(((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) "))},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),(((F,S,a,z,y) * ((F,S,x,0F,y) ")) * ((F,S,x,b,0F) "))] is set
(F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) ")) is Element of the carrier of F
the multF of F . ((F,S,y,a,x),((F,S,a,z,y) * ((F,S,x,0F,y) "))) is Element of the carrier of F
[(F,S,y,a,x),((F,S,a,z,y) * ((F,S,x,0F,y) "))] is set
{(F,S,y,a,x),((F,S,a,z,y) * ((F,S,x,0F,y) "))} is non empty set
{{(F,S,y,a,x),((F,S,a,z,y) * ((F,S,x,0F,y) "))},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),((F,S,a,z,y) * ((F,S,x,0F,y) "))] is set
((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ") is Element of the carrier of F
the multF of F . (((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),((F,S,x,b,0F) ")) is Element of the carrier of F
[((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),((F,S,x,b,0F) ")] is set
{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),((F,S,x,b,0F) ")} is non empty set
{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) ")))} is non empty set
{{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),((F,S,x,b,0F) ")},{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) ")))}} is non empty set
the multF of F . [((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),((F,S,x,b,0F) ")] is set
(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ")) * (F,S,x,b,0F) is Element of the carrier of F
the multF of F . ((((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ")),(F,S,x,b,0F)) is Element of the carrier of F
[(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ")),(F,S,x,b,0F)] is set
{(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ")),(F,S,x,b,0F)} is non empty set
{(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) "))} is non empty set
{{(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ")),(F,S,x,b,0F)},{(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) "))}} is non empty set
the multF of F . [(((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * ((F,S,x,b,0F) ")),(F,S,x,b,0F)] is set
((F,S,x,b,0F) ") * (F,S,x,b,0F) is Element of the carrier of F
the multF of F . (((F,S,x,b,0F) "),(F,S,x,b,0F)) is Element of the carrier of F
[((F,S,x,b,0F) "),(F,S,x,b,0F)] is set
{((F,S,x,b,0F) "),(F,S,x,b,0F)} is non empty set
{((F,S,x,b,0F) ")} is non empty set
{{((F,S,x,b,0F) "),(F,S,x,b,0F)},{((F,S,x,b,0F) ")}} is non empty set
the multF of F . [((F,S,x,b,0F) "),(F,S,x,b,0F)] is set
((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * (((F,S,x,b,0F) ") * (F,S,x,b,0F)) is Element of the carrier of F
the multF of F . (((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(((F,S,x,b,0F) ") * (F,S,x,b,0F))) is Element of the carrier of F
[((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(((F,S,x,b,0F) ") * (F,S,x,b,0F))] is set
{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(((F,S,x,b,0F) ") * (F,S,x,b,0F))} is non empty set
{{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(((F,S,x,b,0F) ") * (F,S,x,b,0F))},{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) ")))}} is non empty set
the multF of F . [((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(((F,S,x,b,0F) ") * (F,S,x,b,0F))] is set
((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))) * (1_ F) is Element of the carrier of F
the multF of F . (((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(1_ F)) is Element of the carrier of F
[((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(1_ F)] is set
{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(1_ F)} is non empty set
{{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(1_ F)},{((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) ")))}} is non empty set
the multF of F . [((F,S,y,a,x) * ((F,S,a,z,y) * ((F,S,x,0F,y) "))),(1_ F)] is set
(F,S,a,z,y) * (F,S,x,y,0F) is Element of the carrier of F
the multF of F . ((F,S,a,z,y),(F,S,x,y,0F)) is Element of the carrier of F
[(F,S,a,z,y),(F,S,x,y,0F)] is set
{(F,S,a,z,y),(F,S,x,y,0F)} is non empty set
{{(F,S,a,z,y),(F,S,x,y,0F)},{(F,S,a,z,y)}} is non empty set
the multF of F . [(F,S,a,z,y),(F,S,x,y,0F)] is set
(F,S,y,a,x) * ((F,S,a,z,y) * (F,S,x,y,0F)) is Element of the carrier of F
the multF of F . ((F,S,y,a,x),((F,S,a,z,y) * (F,S,x,y,0F))) is Element of the carrier of F
[(F,S,y,a,x),((F,S,a,z,y) * (F,S,x,y,0F))] is set
{(F,S,y,a,x),((F,S,a,z,y) * (F,S,x,y,0F))} is non empty set
{{(F,S,y,a,x),((F,S,a,z,y) * (F,S,x,y,0F))},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),((F,S,a,z,y) * (F,S,x,y,0F))] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
(F,S,a,b,x) is Element of the carrier of F
the carrier of F is non empty non trivial set
y is Element of the carrier of S
(F,S,x,a,y) is Element of the carrier of F
(F,S,a,b,x) * (F,S,x,a,y) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,b,x),(F,S,x,a,y)) is Element of the carrier of F
[(F,S,a,b,x),(F,S,x,a,y)] is set
{(F,S,a,b,x),(F,S,x,a,y)} is non empty set
{(F,S,a,b,x)} is non empty set
{{(F,S,a,b,x),(F,S,x,a,y)},{(F,S,a,b,x)}} is non empty set
the multF of F . [(F,S,a,b,x),(F,S,x,a,y)] is set
(F,S,a,b,y) is Element of the carrier of F
(F,S,y,a,x) is Element of the carrier of F
(F,S,a,b,y) * (F,S,y,a,x) is Element of the carrier of F
the multF of F . ((F,S,a,b,y),(F,S,y,a,x)) is Element of the carrier of F
[(F,S,a,b,y),(F,S,y,a,x)] is set
{(F,S,a,b,y),(F,S,y,a,x)} is non empty set
{(F,S,a,b,y)} is non empty set
{{(F,S,a,b,y),(F,S,y,a,x)},{(F,S,a,b,y)}} is non empty set
the multF of F . [(F,S,a,b,y),(F,S,y,a,x)] is set
0. F is V53(F) Element of the carrier of F
1_ F is Element of the carrier of F
K173(F) is V53(F) Element of the carrier of F
(F,S,a,b,x) " is Element of the carrier of F
(F,S,a,b,y) * ((F,S,a,b,x) ") is Element of the carrier of F
the multF of F . ((F,S,a,b,y),((F,S,a,b,x) ")) is Element of the carrier of F
[(F,S,a,b,y),((F,S,a,b,x) ")] is set
{(F,S,a,b,y),((F,S,a,b,x) ")} is non empty set
{{(F,S,a,b,y),((F,S,a,b,x) ")},{(F,S,a,b,y)}} is non empty set
the multF of F . [(F,S,a,b,y),((F,S,a,b,x) ")] is set
(F,S,a,x,y) is Element of the carrier of F
((F,S,a,b,y) * ((F,S,a,b,x) ")) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . (((F,S,a,b,y) * ((F,S,a,b,x) ")),(F,S,a,b,x)) is Element of the carrier of F
[((F,S,a,b,y) * ((F,S,a,b,x) ")),(F,S,a,b,x)] is set
{((F,S,a,b,y) * ((F,S,a,b,x) ")),(F,S,a,b,x)} is non empty set
{((F,S,a,b,y) * ((F,S,a,b,x) "))} is non empty set
{{((F,S,a,b,y) * ((F,S,a,b,x) ")),(F,S,a,b,x)},{((F,S,a,b,y) * ((F,S,a,b,x) "))}} is non empty set
the multF of F . [((F,S,a,b,y) * ((F,S,a,b,x) ")),(F,S,a,b,x)] is set
(F,S,x,y,a) is Element of the carrier of F
(F,S,x,y,a) " is Element of the carrier of F
(F,S,y,x,a) is Element of the carrier of F
((F,S,x,y,a) ") * (F,S,y,x,a) is Element of the carrier of F
the multF of F . (((F,S,x,y,a) "),(F,S,y,x,a)) is Element of the carrier of F
[((F,S,x,y,a) "),(F,S,y,x,a)] is set
{((F,S,x,y,a) "),(F,S,y,x,a)} is non empty set
{((F,S,x,y,a) ")} is non empty set
{{((F,S,x,y,a) "),(F,S,y,x,a)},{((F,S,x,y,a) ")}} is non empty set
the multF of F . [((F,S,x,y,a) "),(F,S,y,x,a)] is set
(((F,S,x,y,a) ") * (F,S,y,x,a)) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . ((((F,S,x,y,a) ") * (F,S,y,x,a)),(F,S,a,b,x)) is Element of the carrier of F
[(((F,S,x,y,a) ") * (F,S,y,x,a)),(F,S,a,b,x)] is set
{(((F,S,x,y,a) ") * (F,S,y,x,a)),(F,S,a,b,x)} is non empty set
{(((F,S,x,y,a) ") * (F,S,y,x,a))} is non empty set
{{(((F,S,x,y,a) ") * (F,S,y,x,a)),(F,S,a,b,x)},{(((F,S,x,y,a) ") * (F,S,y,x,a))}} is non empty set
the multF of F . [(((F,S,x,y,a) ") * (F,S,y,x,a)),(F,S,a,b,x)] is set
((F,S,a,b,x) ") * (F,S,a,b,x) is Element of the carrier of F
the multF of F . (((F,S,a,b,x) "),(F,S,a,b,x)) is Element of the carrier of F
[((F,S,a,b,x) "),(F,S,a,b,x)] is set
{((F,S,a,b,x) "),(F,S,a,b,x)} is non empty set
{((F,S,a,b,x) ")} is non empty set
{{((F,S,a,b,x) "),(F,S,a,b,x)},{((F,S,a,b,x) ")}} is non empty set
the multF of F . [((F,S,a,b,x) "),(F,S,a,b,x)] is set
(F,S,a,b,y) * (((F,S,a,b,x) ") * (F,S,a,b,x)) is Element of the carrier of F
the multF of F . ((F,S,a,b,y),(((F,S,a,b,x) ") * (F,S,a,b,x))) is Element of the carrier of F
[(F,S,a,b,y),(((F,S,a,b,x) ") * (F,S,a,b,x))] is set
{(F,S,a,b,y),(((F,S,a,b,x) ") * (F,S,a,b,x))} is non empty set
{{(F,S,a,b,y),(((F,S,a,b,x) ") * (F,S,a,b,x))},{(F,S,a,b,y)}} is non empty set
the multF of F . [(F,S,a,b,y),(((F,S,a,b,x) ") * (F,S,a,b,x))] is set
(F,S,a,b,y) * (1_ F) is Element of the carrier of F
the multF of F . ((F,S,a,b,y),(1_ F)) is Element of the carrier of F
[(F,S,a,b,y),(1_ F)] is set
{(F,S,a,b,y),(1_ F)} is non empty set
{{(F,S,a,b,y),(1_ F)},{(F,S,a,b,y)}} is non empty set
the multF of F . [(F,S,a,b,y),(1_ F)] is set
(F,S,y,x,a) * ((F,S,x,y,a) ") is Element of the carrier of F
the multF of F . ((F,S,y,x,a),((F,S,x,y,a) ")) is Element of the carrier of F
[(F,S,y,x,a),((F,S,x,y,a) ")] is set
{(F,S,y,x,a),((F,S,x,y,a) ")} is non empty set
{(F,S,y,x,a)} is non empty set
{{(F,S,y,x,a),((F,S,x,y,a) ")},{(F,S,y,x,a)}} is non empty set
the multF of F . [(F,S,y,x,a),((F,S,x,y,a) ")] is set
((F,S,y,x,a) * ((F,S,x,y,a) ")) * (F,S,a,b,x) is Element of the carrier of F
the multF of F . (((F,S,y,x,a) * ((F,S,x,y,a) ")),(F,S,a,b,x)) is Element of the carrier of F
[((F,S,y,x,a) * ((F,S,x,y,a) ")),(F,S,a,b,x)] is set
{((F,S,y,x,a) * ((F,S,x,y,a) ")),(F,S,a,b,x)} is non empty set
{((F,S,y,x,a) * ((F,S,x,y,a) "))} is non empty set
{{((F,S,y,x,a) * ((F,S,x,y,a) ")),(F,S,a,b,x)},{((F,S,y,x,a) * ((F,S,x,y,a) "))}} is non empty set
the multF of F . [((F,S,y,x,a) * ((F,S,x,y,a) ")),(F,S,a,b,x)] is set
((F,S,x,y,a) ") * (F,S,a,b,x) is Element of the carrier of F
the multF of F . (((F,S,x,y,a) "),(F,S,a,b,x)) is Element of the carrier of F
[((F,S,x,y,a) "),(F,S,a,b,x)] is set
{((F,S,x,y,a) "),(F,S,a,b,x)} is non empty set
{{((F,S,x,y,a) "),(F,S,a,b,x)},{((F,S,x,y,a) ")}} is non empty set
the multF of F . [((F,S,x,y,a) "),(F,S,a,b,x)] is set
(F,S,y,x,a) * (((F,S,x,y,a) ") * (F,S,a,b,x)) is Element of the carrier of F
the multF of F . ((F,S,y,x,a),(((F,S,x,y,a) ") * (F,S,a,b,x))) is Element of the carrier of F
[(F,S,y,x,a),(((F,S,x,y,a) ") * (F,S,a,b,x))] is set
{(F,S,y,x,a),(((F,S,x,y,a) ") * (F,S,a,b,x))} is non empty set
{{(F,S,y,x,a),(((F,S,x,y,a) ") * (F,S,a,b,x))},{(F,S,y,x,a)}} is non empty set
the multF of F . [(F,S,y,x,a),(((F,S,x,y,a) ") * (F,S,a,b,x))] is set
(F,S,y,a,x) * (F,S,a,b,y) is Element of the carrier of F
the multF of F . ((F,S,y,a,x),(F,S,a,b,y)) is Element of the carrier of F
[(F,S,y,a,x),(F,S,a,b,y)] is set
{(F,S,y,a,x),(F,S,a,b,y)} is non empty set
{(F,S,y,a,x)} is non empty set
{{(F,S,y,a,x),(F,S,a,b,y)},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),(F,S,a,b,y)] is set
(F,S,y,a,x) " is Element of the carrier of F
((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x)) is Element of the carrier of F
the multF of F . (((F,S,y,a,x) "),(((F,S,x,y,a) ") * (F,S,a,b,x))) is Element of the carrier of F
[((F,S,y,a,x) "),(((F,S,x,y,a) ") * (F,S,a,b,x))] is set
{((F,S,y,a,x) "),(((F,S,x,y,a) ") * (F,S,a,b,x))} is non empty set
{((F,S,y,a,x) ")} is non empty set
{{((F,S,y,a,x) "),(((F,S,x,y,a) ") * (F,S,a,b,x))},{((F,S,y,a,x) ")}} is non empty set
the multF of F . [((F,S,y,a,x) "),(((F,S,x,y,a) ") * (F,S,a,b,x))] is set
(F,S,y,a,x) * (((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x))) is Element of the carrier of F
the multF of F . ((F,S,y,a,x),(((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x)))) is Element of the carrier of F
[(F,S,y,a,x),(((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x)))] is set
{(F,S,y,a,x),(((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x)))} is non empty set
{{(F,S,y,a,x),(((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x)))},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),(((F,S,y,a,x) ") * (((F,S,x,y,a) ") * (F,S,a,b,x)))] is set
(F,S,y,a,x) * ((F,S,y,a,x) ") is Element of the carrier of F
the multF of F . ((F,S,y,a,x),((F,S,y,a,x) ")) is Element of the carrier of F
[(F,S,y,a,x),((F,S,y,a,x) ")] is set
{(F,S,y,a,x),((F,S,y,a,x) ")} is non empty set
{{(F,S,y,a,x),((F,S,y,a,x) ")},{(F,S,y,a,x)}} is non empty set
the multF of F . [(F,S,y,a,x),((F,S,y,a,x) ")] is set
((F,S,y,a,x) * ((F,S,y,a,x) ")) * (((F,S,x,y,a) ") * (F,S,a,b,x)) is Element of the carrier of F
the multF of F . (((F,S,y,a,x) * ((F,S,y,a,x) ")),(((F,S,x,y,a) ") * (F,S,a,b,x))) is Element of the carrier of F
[((F,S,y,a,x) * ((F,S,y,a,x) ")),(((F,S,x,y,a) ") * (F,S,a,b,x))] is set
{((F,S,y,a,x) * ((F,S,y,a,x) ")),(((F,S,x,y,a) ") * (F,S,a,b,x))} is non empty set
{((F,S,y,a,x) * ((F,S,y,a,x) "))} is non empty set
{{((F,S,y,a,x) * ((F,S,y,a,x) ")),(((F,S,x,y,a) ") * (F,S,a,b,x))},{((F,S,y,a,x) * ((F,S,y,a,x) "))}} is non empty set
the multF of F . [((F,S,y,a,x) * ((F,S,y,a,x) ")),(((F,S,x,y,a) ") * (F,S,a,b,x))] is set
(((F,S,x,y,a) ") * (F,S,a,b,x)) * (1_ F) is Element of the carrier of F
the multF of F . ((((F,S,x,y,a) ") * (F,S,a,b,x)),(1_ F)) is Element of the carrier of F
[(((F,S,x,y,a) ") * (F,S,a,b,x)),(1_ F)] is set
{(((F,S,x,y,a) ") * (F,S,a,b,x)),(1_ F)} is non empty set
{(((F,S,x,y,a) ") * (F,S,a,b,x))} is non empty set
{{(((F,S,x,y,a) ") * (F,S,a,b,x)),(1_ F)},{(((F,S,x,y,a) ") * (F,S,a,b,x))}} is non empty set
the multF of F . [(((F,S,x,y,a) ") * (F,S,a,b,x)),(1_ F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
y is Element of the carrier of S
x is Element of the carrier of S
b is Element of the carrier of S
the carrier of F is non empty non trivial set
a is Element of the carrier of S
0. F is V53(F) Element of the carrier of F
z is Element of the carrier of S
(F,S,x,y,z) is Element of the carrier of F
(F,S,z,x,b) is Element of the carrier of F
(F,S,x,y,z) * (F,S,z,x,b) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,x,y,z),(F,S,z,x,b)) is Element of the carrier of F
[(F,S,x,y,z),(F,S,z,x,b)] is set
{(F,S,x,y,z),(F,S,z,x,b)} is non empty set
{(F,S,x,y,z)} is non empty set
{{(F,S,x,y,z),(F,S,z,x,b)},{(F,S,x,y,z)}} is non empty set
the multF of F . [(F,S,x,y,z),(F,S,z,x,b)] is set
(F,S,b,z,a) is Element of the carrier of F
((F,S,x,y,z) * (F,S,z,x,b)) * (F,S,b,z,a) is Element of the carrier of F
the multF of F . (((F,S,x,y,z) * (F,S,z,x,b)),(F,S,b,z,a)) is Element of the carrier of F
[((F,S,x,y,z) * (F,S,z,x,b)),(F,S,b,z,a)] is set
{((F,S,x,y,z) * (F,S,z,x,b)),(F,S,b,z,a)} is non empty set
{((F,S,x,y,z) * (F,S,z,x,b))} is non empty set
{{((F,S,x,y,z) * (F,S,z,x,b)),(F,S,b,z,a)},{((F,S,x,y,z) * (F,S,z,x,b))}} is non empty set
the multF of F . [((F,S,x,y,z) * (F,S,z,x,b)),(F,S,b,z,a)] is set
0F is Element of the carrier of S
(F,S,x,y,0F) is Element of the carrier of F
(F,S,0F,x,b) is Element of the carrier of F
(F,S,x,y,0F) * (F,S,0F,x,b) is Element of the carrier of F
the multF of F . ((F,S,x,y,0F),(F,S,0F,x,b)) is Element of the carrier of F
[(F,S,x,y,0F),(F,S,0F,x,b)] is set
{(F,S,x,y,0F),(F,S,0F,x,b)} is non empty set
{(F,S,x,y,0F)} is non empty set
{{(F,S,x,y,0F),(F,S,0F,x,b)},{(F,S,x,y,0F)}} is non empty set
the multF of F . [(F,S,x,y,0F),(F,S,0F,x,b)] is set
(F,S,b,0F,a) is Element of the carrier of F
((F,S,x,y,0F) * (F,S,0F,x,b)) * (F,S,b,0F,a) is Element of the carrier of F
the multF of F . (((F,S,x,y,0F) * (F,S,0F,x,b)),(F,S,b,0F,a)) is Element of the carrier of F
[((F,S,x,y,0F) * (F,S,0F,x,b)),(F,S,b,0F,a)] is set
{((F,S,x,y,0F) * (F,S,0F,x,b)),(F,S,b,0F,a)} is non empty set
{((F,S,x,y,0F) * (F,S,0F,x,b))} is non empty set
{{((F,S,x,y,0F) * (F,S,0F,x,b)),(F,S,b,0F,a)},{((F,S,x,y,0F) * (F,S,0F,x,b))}} is non empty set
the multF of F . [((F,S,x,y,0F) * (F,S,0F,x,b)),(F,S,b,0F,a)] is set
z is Element of the carrier of F
0F is Element of the carrier of F
p is Element of the carrier of S
r is Element of the carrier of S
(F,S,x,y,r) is Element of the carrier of F
(F,S,r,x,b) is Element of the carrier of F
(F,S,x,y,r) * (F,S,r,x,b) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,x,y,r),(F,S,r,x,b)) is Element of the carrier of F
[(F,S,x,y,r),(F,S,r,x,b)] is set
{(F,S,x,y,r),(F,S,r,x,b)} is non empty set
{(F,S,x,y,r)} is non empty set
{{(F,S,x,y,r),(F,S,r,x,b)},{(F,S,x,y,r)}} is non empty set
the multF of F . [(F,S,x,y,r),(F,S,r,x,b)] is set
(F,S,b,r,a) is Element of the carrier of F
((F,S,x,y,r) * (F,S,r,x,b)) * (F,S,b,r,a) is Element of the carrier of F
the multF of F . (((F,S,x,y,r) * (F,S,r,x,b)),(F,S,b,r,a)) is Element of the carrier of F
[((F,S,x,y,r) * (F,S,r,x,b)),(F,S,b,r,a)] is set
{((F,S,x,y,r) * (F,S,r,x,b)),(F,S,b,r,a)} is non empty set
{((F,S,x,y,r) * (F,S,r,x,b))} is non empty set
{{((F,S,x,y,r) * (F,S,r,x,b)),(F,S,b,r,a)},{((F,S,x,y,r) * (F,S,r,x,b))}} is non empty set
the multF of F . [((F,S,x,y,r) * (F,S,r,x,b)),(F,S,b,r,a)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
0. F is V53(F) Element of the carrier of F
the carrier of F is non empty non trivial set
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
0. S is V53(S) Element of the carrier of S
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of S
(F,S,x,y,a,b) is Element of the carrier of F
z is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
0. F is V53(F) Element of the carrier of F
the carrier of F is non empty non trivial set
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of S
(F,S,x,y,a,b) is Element of the carrier of F
0. S is V53(S) Element of the carrier of S
0F is Element of the carrier of S
(F,S,0F,a,x) is Element of the carrier of F
(F,S,a,b,0F) is Element of the carrier of F
(F,S,a,b,0F) * (F,S,0F,a,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,b,0F),(F,S,0F,a,x)) is Element of the carrier of F
[(F,S,a,b,0F),(F,S,0F,a,x)] is set
{(F,S,a,b,0F),(F,S,0F,a,x)} is non empty set
{(F,S,a,b,0F)} is non empty set
{{(F,S,a,b,0F),(F,S,0F,a,x)},{(F,S,a,b,0F)}} is non empty set
the multF of F . [(F,S,a,b,0F),(F,S,0F,a,x)] is set
(F,S,x,0F,y) is Element of the carrier of F
((F,S,a,b,0F) * (F,S,0F,a,x)) * (F,S,x,0F,y) is Element of the carrier of F
the multF of F . (((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)) is Element of the carrier of F
[((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)] is set
{((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)} is non empty set
{((F,S,a,b,0F) * (F,S,0F,a,x))} is non empty set
{{((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)},{((F,S,a,b,0F) * (F,S,0F,a,x))}} is non empty set
the multF of F . [((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)] is set
0F is Element of the carrier of S
0F is Element of the carrier of S
0F is Element of the carrier of S
0F is Element of the carrier of S
(F,S,x,0F,y) is Element of the carrier of F
(F,S,a,b,0F) is Element of the carrier of F
(F,S,0F,a,x) is Element of the carrier of F
(F,S,a,b,0F) * (F,S,0F,a,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,b,0F),(F,S,0F,a,x)) is Element of the carrier of F
[(F,S,a,b,0F),(F,S,0F,a,x)] is set
{(F,S,a,b,0F),(F,S,0F,a,x)} is non empty set
{(F,S,a,b,0F)} is non empty set
{{(F,S,a,b,0F),(F,S,0F,a,x)},{(F,S,a,b,0F)}} is non empty set
the multF of F . [(F,S,a,b,0F),(F,S,0F,a,x)] is set
((F,S,a,b,0F) * (F,S,0F,a,x)) * (F,S,x,0F,y) is Element of the carrier of F
the multF of F . (((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)) is Element of the carrier of F
[((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)] is set
{((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)} is non empty set
{((F,S,a,b,0F) * (F,S,0F,a,x))} is non empty set
{{((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)},{((F,S,a,b,0F) * (F,S,0F,a,x))}} is non empty set
the multF of F . [((F,S,a,b,0F) * (F,S,0F,a,x)),(F,S,x,0F,y)] is set
0F is Element of the carrier of S
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of S
(F,S,x,y,a,b) is Element of the carrier of F
the carrier of F is non empty non trivial set
(F,S,y,x,a,b) is Element of the carrier of F
0. S is V53(S) Element of the carrier of S
z is Element of the carrier of S
z is Element of the carrier of S
(F,S,a,b,z) is Element of the carrier of F
(F,S,z,a,y) is Element of the carrier of F
(F,S,a,b,z) * (F,S,z,a,y) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . ((F,S,a,b,z),(F,S,z,a,y)) is Element of the carrier of F
[(F,S,a,b,z),(F,S,z,a,y)] is set
{(F,S,a,b,z),(F,S,z,a,y)} is non empty set
{(F,S,a,b,z)} is non empty set
{{(F,S,a,b,z),(F,S,z,a,y)},{(F,S,a,b,z)}} is non empty set
the multF of F . [(F,S,a,b,z),(F,S,z,a,y)] is set
(F,S,y,z,x) is Element of the carrier of F
((F,S,a,b,z) * (F,S,z,a,y)) * (F,S,y,z,x) is Element of the carrier of F
the multF of F . (((F,S,a,b,z) * (F,S,z,a,y)),(F,S,y,z,x)) is Element of the carrier of F
[((F,S,a,b,z) * (F,S,z,a,y)),(F,S,y,z,x)] is set
{((F,S,a,b,z) * (F,S,z,a,y)),(F,S,y,z,x)} is non empty set
{((F,S,a,b,z) * (F,S,z,a,y))} is non empty set
{{((F,S,a,b,z) * (F,S,z,a,y)),(F,S,y,z,x)},{((F,S,a,b,z) * (F,S,z,a,y))}} is non empty set
the multF of F . [((F,S,a,b,z) * (F,S,z,a,y)),(F,S,y,z,x)] is set
(F,S,z,a,y) * (F,S,y,z,x) is Element of the carrier of F
the multF of F . ((F,S,z,a,y),(F,S,y,z,x)) is Element of the carrier of F
[(F,S,z,a,y),(F,S,y,z,x)] is set
{(F,S,z,a,y),(F,S,y,z,x)} is non empty set
{(F,S,z,a,y)} is non empty set
{{(F,S,z,a,y),(F,S,y,z,x)},{(F,S,z,a,y)}} is non empty set
the multF of F . [(F,S,z,a,y),(F,S,y,z,x)] is set
(F,S,a,b,z) * ((F,S,z,a,y) * (F,S,y,z,x)) is Element of the carrier of F
the multF of F . ((F,S,a,b,z),((F,S,z,a,y) * (F,S,y,z,x))) is Element of the carrier of F
[(F,S,a,b,z),((F,S,z,a,y) * (F,S,y,z,x))] is set
{(F,S,a,b,z),((F,S,z,a,y) * (F,S,y,z,x))} is non empty set
{{(F,S,a,b,z),((F,S,z,a,y) * (F,S,y,z,x))},{(F,S,a,b,z)}} is non empty set
the multF of F . [(F,S,a,b,z),((F,S,z,a,y) * (F,S,y,z,x))] is set
(F,S,z,a,x) is Element of the carrier of F
(F,S,x,z,y) is Element of the carrier of F
(F,S,z,a,x) * (F,S,x,z,y) is Element of the carrier of F
the multF of F . ((F,S,z,a,x),(F,S,x,z,y)) is Element of the carrier of F
[(F,S,z,a,x),(F,S,x,z,y)] is set
{(F,S,z,a,x),(F,S,x,z,y)} is non empty set
{(F,S,z,a,x)} is non empty set
{{(F,S,z,a,x),(F,S,x,z,y)},{(F,S,z,a,x)}} is non empty set
the multF of F . [(F,S,z,a,x),(F,S,x,z,y)] is set
(F,S,a,b,z) * ((F,S,z,a,x) * (F,S,x,z,y)) is Element of the carrier of F
the multF of F . ((F,S,a,b,z),((F,S,z,a,x) * (F,S,x,z,y))) is Element of the carrier of F
[(F,S,a,b,z),((F,S,z,a,x) * (F,S,x,z,y))] is set
{(F,S,a,b,z),((F,S,z,a,x) * (F,S,x,z,y))} is non empty set
{{(F,S,a,b,z),((F,S,z,a,x) * (F,S,x,z,y))},{(F,S,a,b,z)}} is non empty set
the multF of F . [(F,S,a,b,z),((F,S,z,a,x) * (F,S,x,z,y))] is set
(F,S,a,b,z) * (F,S,z,a,x) is Element of the carrier of F
the multF of F . ((F,S,a,b,z),(F,S,z,a,x)) is Element of the carrier of F
[(F,S,a,b,z),(F,S,z,a,x)] is set
{(F,S,a,b,z),(F,S,z,a,x)} is non empty set
{{(F,S,a,b,z),(F,S,z,a,x)},{(F,S,a,b,z)}} is non empty set
the multF of F . [(F,S,a,b,z),(F,S,z,a,x)] is set
((F,S,a,b,z) * (F,S,z,a,x)) * (F,S,x,z,y) is Element of the carrier of F
the multF of F . (((F,S,a,b,z) * (F,S,z,a,x)),(F,S,x,z,y)) is Element of the carrier of F
[((F,S,a,b,z) * (F,S,z,a,x)),(F,S,x,z,y)] is set
{((F,S,a,b,z) * (F,S,z,a,x)),(F,S,x,z,y)} is non empty set
{((F,S,a,b,z) * (F,S,z,a,x))} is non empty set
{{((F,S,a,b,z) * (F,S,z,a,x)),(F,S,x,z,y)},{((F,S,a,b,z) * (F,S,z,a,x))}} is non empty set
the multF of F . [((F,S,a,b,z) * (F,S,z,a,x)),(F,S,x,z,y)] is set
0. F is V53(F) Element of the carrier of F
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
the carrier of F is non empty non trivial set
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of S
(F,S,x,y,a,b) is Element of the carrier of F
z is Element of the carrier of F
z * y is Element of the carrier of S
(F,S,x,(z * y),a,b) is Element of the carrier of F
z * (F,S,x,y,a,b) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the multF of F . (z,(F,S,x,y,a,b)) is Element of the carrier of F
[z,(F,S,x,y,a,b)] is set
{z,(F,S,x,y,a,b)} is non empty set
{z} is non empty set
{{z,(F,S,x,y,a,b)},{z}} is non empty set
the multF of F . [z,(F,S,x,y,a,b)] is set
0. F is V53(F) Element of the carrier of F
0. S is V53(S) Element of the carrier of S
p is Element of the carrier of S
p is Element of the carrier of S
(F,S,a,b,p) is Element of the carrier of F
(F,S,p,a,x) is Element of the carrier of F
(F,S,a,b,p) * (F,S,p,a,x) is Element of the carrier of F
the multF of F . ((F,S,a,b,p),(F,S,p,a,x)) is Element of the carrier of F
[(F,S,a,b,p),(F,S,p,a,x)] is set
{(F,S,a,b,p),(F,S,p,a,x)} is non empty set
{(F,S,a,b,p)} is non empty set
{{(F,S,a,b,p),(F,S,p,a,x)},{(F,S,a,b,p)}} is non empty set
the multF of F . [(F,S,a,b,p),(F,S,p,a,x)] is set
(F,S,x,p,(z * y)) is Element of the carrier of F
((F,S,a,b,p) * (F,S,p,a,x)) * (F,S,x,p,(z * y)) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(z * y))) is Element of the carrier of F
[((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(z * y))] is set
{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(z * y))} is non empty set
{((F,S,a,b,p) * (F,S,p,a,x))} is non empty set
{{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(z * y))},{((F,S,a,b,p) * (F,S,p,a,x))}} is non empty set
the multF of F . [((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(z * y))] is set
(F,S,x,p,y) is Element of the carrier of F
z * (F,S,x,p,y) is Element of the carrier of F
the multF of F . (z,(F,S,x,p,y)) is Element of the carrier of F
[z,(F,S,x,p,y)] is set
{z,(F,S,x,p,y)} is non empty set
{{z,(F,S,x,p,y)},{z}} is non empty set
the multF of F . [z,(F,S,x,p,y)] is set
(z * (F,S,x,p,y)) * ((F,S,a,b,p) * (F,S,p,a,x)) is Element of the carrier of F
the multF of F . ((z * (F,S,x,p,y)),((F,S,a,b,p) * (F,S,p,a,x))) is Element of the carrier of F
[(z * (F,S,x,p,y)),((F,S,a,b,p) * (F,S,p,a,x))] is set
{(z * (F,S,x,p,y)),((F,S,a,b,p) * (F,S,p,a,x))} is non empty set
{(z * (F,S,x,p,y))} is non empty set
{{(z * (F,S,x,p,y)),((F,S,a,b,p) * (F,S,p,a,x))},{(z * (F,S,x,p,y))}} is non empty set
the multF of F . [(z * (F,S,x,p,y)),((F,S,a,b,p) * (F,S,p,a,x))] is set
((F,S,a,b,p) * (F,S,p,a,x)) * (F,S,x,p,y) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)) is Element of the carrier of F
[((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)] is set
{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)} is non empty set
{{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)},{((F,S,a,b,p) * (F,S,p,a,x))}} is non empty set
the multF of F . [((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)] is set
z * (0. F) is Element of the carrier of F
the multF of F . (z,(0. F)) is Element of the carrier of F
[z,(0. F)] is set
{z,(0. F)} is non empty set
{{z,(0. F)},{z}} is non empty set
the multF of F . [z,(0. F)] is set
F is non empty non degenerated non trivial right_complementable almost_left_invertible Abelian add-associative right_zeroed unital associative commutative right-distributive left-distributive right_unital well-unital V116() left_unital doubleLoopStr
S is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital (F) SymStr over F
the carrier of S is non empty set
b is Element of the carrier of S
a is Element of the carrier of S
x is Element of the carrier of S
y is Element of the carrier of S
(F,S,x,y,a,b) is Element of the carrier of F
the carrier of F is non empty non trivial set
z is Element of the carrier of S
y + z is Element of the carrier of S
the addF of S is V1() V4([: the carrier of S, the carrier of S:]) V5( the carrier of S) Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . (y,z) is Element of the carrier of S
[y,z] is set
{y,z} is non empty set
{y} is non empty set
{{y,z},{y}} is non empty set
the addF of S . [y,z] is set
(F,S,x,(y + z),a,b) is Element of the carrier of F
(F,S,x,z,a,b) is Element of the carrier of F
(F,S,x,y,a,b) + (F,S,x,z,a,b) is Element of the carrier of F
the addF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
[: the carrier of F, the carrier of F:] is non empty set
[:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
bool [:[: the carrier of F, the carrier of F:], the carrier of F:] is non empty set
the addF of F . ((F,S,x,y,a,b),(F,S,x,z,a,b)) is Element of the carrier of F
[(F,S,x,y,a,b),(F,S,x,z,a,b)] is set
{(F,S,x,y,a,b),(F,S,x,z,a,b)} is non empty set
{(F,S,x,y,a,b)} is non empty set
{{(F,S,x,y,a,b),(F,S,x,z,a,b)},{(F,S,x,y,a,b)}} is non empty set
the addF of F . [(F,S,x,y,a,b),(F,S,x,z,a,b)] is set
0. F is V53(F) Element of the carrier of F
0. S is V53(S) Element of the carrier of S
p is Element of the carrier of S
p is Element of the carrier of S
(F,S,a,b,p) is Element of the carrier of F
(F,S,p,a,x) is Element of the carrier of F
(F,S,a,b,p) * (F,S,p,a,x) is Element of the carrier of F
the multF of F is V1() V4([: the carrier of F, the carrier of F:]) V5( the carrier of F) Function-like V18([: the carrier of F, the carrier of F:], the carrier of F) Element of bool [:[: the carrier of F, the carrier of F:], the carrier of F:]
the multF of F . ((F,S,a,b,p),(F,S,p,a,x)) is Element of the carrier of F
[(F,S,a,b,p),(F,S,p,a,x)] is set
{(F,S,a,b,p),(F,S,p,a,x)} is non empty set
{(F,S,a,b,p)} is non empty set
{{(F,S,a,b,p),(F,S,p,a,x)},{(F,S,a,b,p)}} is non empty set
the multF of F . [(F,S,a,b,p),(F,S,p,a,x)] is set
(F,S,x,p,(y + z)) is Element of the carrier of F
((F,S,a,b,p) * (F,S,p,a,x)) * (F,S,x,p,(y + z)) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(y + z))) is Element of the carrier of F
[((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(y + z))] is set
{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(y + z))} is non empty set
{((F,S,a,b,p) * (F,S,p,a,x))} is non empty set
{{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(y + z))},{((F,S,a,b,p) * (F,S,p,a,x))}} is non empty set
the multF of F . [((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,(y + z))] is set
(F,S,x,p,y) is Element of the carrier of F
((F,S,a,b,p) * (F,S,p,a,x)) * (F,S,x,p,y) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)) is Element of the carrier of F
[((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)] is set
{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)} is non empty set
{{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)},{((F,S,a,b,p) * (F,S,p,a,x))}} is non empty set
the multF of F . [((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,y)] is set
(F,S,x,p,z) is Element of the carrier of F
((F,S,a,b,p) * (F,S,p,a,x)) * (F,S,x,p,z) is Element of the carrier of F
the multF of F . (((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,z)) is Element of the carrier of F
[((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,z)] is set
{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,z)} is non empty set
{{((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,z)},{((F,S,a,b,p) * (F,S,p,a,x))}} is non empty set
the multF of F . [((F,S,a,b,p) * (F,S,p,a,x)),(F,S,x,p,z)] is set
(F,S,x,p,y) + (F,S,x,p,z) is Element of the carrier of F
the addF of F . ((F,S,x,p,y),(F,S,x,p,z)) is Element of the carrier of F
[(F,S,x,p,y),(F,S,x,p,z)] is set
{(F,S,x,p,y),(F,S,x,p,z)} is non empty set
{(F,S,x,p,y)} is non empty set
{{(F,S,x,p,y),(F,S,x,p,z)},{(F,S,x,p,y)}} is non empty set
the addF of F . [(F,S,x,p,y),(F,S,x,p,z)] is set