:: BSPACE semantic presentation

REAL is set
NAT is non empty non trivial V23() V24() V25() non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
NAT is non empty non trivial V23() V24() V25() non finite cardinal limit_cardinal set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set

RAT is set
INT is set

2 is non empty V23() V24() V25() V29() finite cardinal V57() integer ext-real positive V128() Element of NAT
1 is non empty V23() V24() V25() V29() finite cardinal V57() integer ext-real positive V128() Element of NAT

K385(0,1,2) is non empty finite set
[:K385(0,1,2),K385(0,1,2):] is non empty finite set
[:[:K385(0,1,2),K385(0,1,2):],K385(0,1,2):] is non empty finite set
bool [:[:K385(0,1,2),K385(0,1,2):],K385(0,1,2):] is non empty finite V34() set
bool [:K385(0,1,2),K385(0,1,2):] is non empty finite V34() set

bool is non empty set

K444(1,INT) is V57() integer ext-real V128() Element of INT
K444(0,INT) is V57() integer ext-real V128() Element of INT
doubleLoopStr(# INT,K587(),K589(),K444(1,INT),K444(0,INT) #) is strict doubleLoopStr
the carrier of INT.Ring is set
[: the carrier of INT.Ring,NAT:] is set
bool [: the carrier of INT.Ring,NAT:] is non empty set

bool is non empty set
K532() is non empty strict multMagma
the carrier of K532() is non empty set

bool is non empty set

bool is non empty set

bool is non empty set

bool is non empty set
bool is non empty set
is non empty non trivial non finite set
is non empty non trivial non finite set
bool is non empty non trivial non finite set
3 is non empty V23() V24() V25() V29() finite cardinal V57() integer ext-real positive V128() Element of NAT
bool {} is non empty finite V34() set
is non empty trivial finite V34() 1 -element set
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
{ b1 where b1 is V23() V24() V25() V29() finite cardinal V57() integer ext-real V128() Element of NAT : ( 1 <= b1 & b1 <= 1 ) } is set
{1} is non empty trivial finite V34() 1 -element set
Seg 2 is non empty finite 2 -element Element of bool NAT
{ b1 where b1 is V23() V24() V25() V29() finite cardinal V57() integer ext-real V128() Element of NAT : ( 1 <= b1 & b1 <= 2 ) } is set
{1,2} is non empty finite V34() set
{{},1} is non empty finite V34() set
X is 1-sorted
[#] X is non proper Element of bool the carrier of X
the carrier of X is set
bool the carrier of X is non empty set

X is 1-sorted
the carrier of X is set
f is V23() V24() V25() V29() finite cardinal V57() integer ext-real V128() Element of NAT

dom x1 is finite Element of bool NAT
x1 . f is set
X is 1-sorted
the carrier of X is set

x1 is V23() V24() V25() V29() finite cardinal V57() integer ext-real V128() set
f . x1 is set
F1() is 1-sorted
(F1()) is Relation-like NAT -defined the carrier of F1() -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of F1()
the carrier of F1() is set
[#] F1() is non proper Element of bool the carrier of F1()
bool the carrier of F1() is non empty set

Segm 2 is Element of bool NAT
K533(2) is Relation-like [:(Segm 2),(Segm 2):] -defined Segm 2 -valued Function-like V18([:(Segm 2),(Segm 2):], Segm 2) Element of bool [:[:(Segm 2),(Segm 2):],(Segm 2):]
[:(Segm 2),(Segm 2):] is set
[:[:(Segm 2),(Segm 2):],(Segm 2):] is set
bool [:[:(Segm 2),(Segm 2):],(Segm 2):] is non empty set
K505(2) is Relation-like [:(Segm 2),(Segm 2):] -defined Segm 2 -valued Function-like V18([:(Segm 2),(Segm 2):], Segm 2) Element of bool [:[:(Segm 2),(Segm 2):],(Segm 2):]
K444(1,(Segm 2)) is Element of Segm 2
K444(0,(Segm 2)) is Element of Segm 2
doubleLoopStr(# (Segm 2),K533(2),K505(2),K444(1,(Segm 2)),K444(0,(Segm 2)) #) is strict doubleLoopStr

[#] () is non empty non proper Element of bool the carrier of ()
the carrier of () is non empty non trivial set
bool the carrier of () is non empty set
X is Element of the carrier of ()
0. () is V50(()) Element of the carrier of ()
the ZeroF of () is Element of the carrier of ()
1. () is V50(()) Element of the carrier of ()
the OneF of () is Element of the carrier of ()
(1. ()) + (1. ()) is Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like V18([: the carrier of (), the carrier of ():], the carrier of ()) Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . ((1. ()),(1. ())) is Element of the carrier of ()
[(1. ()),(1. ())] is set
{(1. ()),(1. ())} is non empty finite set
{(1. ())} is non empty trivial finite 1 -element set
{{(1. ()),(1. ())},{(1. ())}} is non empty finite V34() set
the addF of () . [(1. ()),(1. ())] is set
1 + 1 is V23() V24() V25() V29() finite cardinal V57() integer ext-real V128() Element of NAT
(1 + 1) mod 2 is V57() integer ext-real V128() set
X is Element of the carrier of ()
f is Element of the carrier of ()
f is set
X is set
X is set
f is set
(X,f) is Element of the carrier of ()
x2 is set
x1 is set
(x1,x2) is Element of the carrier of ()
X is set
f is set
(X,f) is Element of the carrier of ()
x2 is set
x1 is set
(x1,x2) is Element of the carrier of ()
X is set
f is set
(X,f) is Element of the carrier of ()
x1 is set
x2 is set
(x1,x2) is Element of the carrier of ()
X is set
f is set
(X,f) is Element of the carrier of ()
x1 is set
(X,x1) is Element of the carrier of ()
X is set
x1 is set
(X,x1) is Element of the carrier of ()
f is set
(f,x1) is Element of the carrier of ()
X is set
({},X) is Element of the carrier of ()
X is set
bool X is non empty set
f is Element of bool X
x1 is Element of bool X
f \+\ x1 is Element of bool X
f \ x1 is set
x1 \ f is set
(f \ x1) \/ (x1 \ f) is set
x2 is Element of X
((f \+\ x1),x2) is Element of the carrier of ()
(f,x2) is Element of the carrier of ()
(x1,x2) is Element of the carrier of ()
(f,x2) + (x1,x2) is Element of the carrier of ()
the addF of () . ((f,x2),(x1,x2)) is Element of the carrier of ()
[(f,x2),(x1,x2)] is set
{(f,x2),(x1,x2)} is non empty finite set
{(f,x2)} is non empty trivial finite 1 -element set
{{(f,x2),(x1,x2)},{(f,x2)}} is non empty finite V34() set
the addF of () . [(f,x2),(x1,x2)] is set
X is set
f is set
x1 is set
(X,x1) is Element of the carrier of ()
(f,x1) is Element of the carrier of ()
x1 is set
(X,x1) is Element of the carrier of ()
(f,x1) is Element of the carrier of ()
x1 is set
(f,x1) is Element of the carrier of ()
(X,x1) is Element of the carrier of ()
X is set
bool X is non empty set
f is Element of the carrier of ()
x1 is Element of bool X

x2 is Element of bool X
X is set
bool X is non empty set
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set
f is set
x1 is set
x2 is Element of bool X
y is Element of bool X
x2 \+\ y is Element of bool X
x2 \ y is set
y \ x2 is set
(x2 \ y) \/ (y \ x2) is set
f is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
x1 is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
x2 is Element of bool X
y is Element of bool X
x1 . (x2,y) is Element of bool X
[x2,y] is set
{x2,y} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,y},{x2}} is non empty finite V34() set
x1 . [x2,y] is set
x2 \+\ y is Element of bool X
x2 \ y is set
y \ x2 is set
(x2 \ y) \/ (y \ x2) is set
x is Element of bool X
A is Element of bool X
x \+\ A is Element of bool X
x \ A is set
A \ x is set
(x \ A) \/ (A \ x) is set
x2 is Element of bool X
y is Element of bool X
x1 . (x2,y) is Element of bool X
[x2,y] is set
{x2,y} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,y},{x2}} is non empty finite V34() set
x1 . [x2,y] is set
x2 \+\ y is Element of bool X
x2 \ y is set
y \ x2 is set
(x2 \ y) \/ (y \ x2) is set
f is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
x1 is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
dom f is Relation-like bool X -defined bool X -valued Element of bool [:(bool X),(bool X):]
bool [:(bool X),(bool X):] is non empty set
x2 is set
f . x2 is set
x1 . x2 is set
y is set
x is set
[y,x] is set
{y,x} is non empty finite set
{y} is non empty trivial finite 1 -element set
{{y,x},{y}} is non empty finite V34() set
l is Element of bool X
A is Element of bool X
f . (l,A) is Element of bool X
[l,A] is set
{l,A} is non empty finite set
{l} is non empty trivial finite 1 -element set
{{l,A},{l}} is non empty finite V34() set
f . [l,A] is set
l \+\ A is Element of bool X
l \ A is set
A \ l is set
(l \ A) \/ (A \ l) is set
x1 . (l,A) is Element of bool X
x1 . [l,A] is set
dom x1 is Relation-like bool X -defined bool X -valued Element of bool [:(bool X),(bool X):]
X is set
bool X is non empty set
f is Element of the carrier of ()
x1 is Element of bool X
x2 is Element of bool X
x1 \+\ x2 is Element of bool X
x1 \ x2 is set
x2 \ x1 is set
(x1 \ x2) \/ (x2 \ x1) is set
(X,f,(x1 \+\ x2)) is Element of bool X
(X,f,x1) is Element of bool X
(X,f,x2) is Element of bool X
(X,f,x1) \+\ (X,f,x2) is Element of bool X
(X,f,x1) \ (X,f,x2) is set
(X,f,x2) \ (X,f,x1) is set
((X,f,x1) \ (X,f,x2)) \/ ((X,f,x2) \ (X,f,x1)) is set

X is set
bool X is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of ()
f + x1 is Element of the carrier of ()
the addF of () . (f,x1) is Element of the carrier of ()
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the addF of () . [f,x1] is set
x2 is Element of bool X
(X,(f + x1),x2) is Element of bool X
(X,f,x2) is Element of bool X
(X,x1,x2) is Element of bool X
(X,f,x2) \+\ (X,x1,x2) is Element of bool X
(X,f,x2) \ (X,x1,x2) is set
(X,x1,x2) \ (X,f,x2) is set
((X,f,x2) \ (X,x1,x2)) \/ ((X,x1,x2) \ (X,f,x2)) is set

x2 \+\ x2 is Element of bool X
x2 \ x2 is set
(x2 \ x2) \/ (x2 \ x2) is set

X is set
bool X is non empty set
f is Element of bool X
(X,(1. ()),f) is Element of bool X
X is set
bool X is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of ()
f * x1 is Element of the carrier of ()
the multF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like V18([: the carrier of (), the carrier of ():], the carrier of ()) Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
the multF of () . (f,x1) is Element of the carrier of ()
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the multF of () . [f,x1] is set
x2 is Element of bool X
(X,x1,x2) is Element of bool X
(X,f,(X,x1,x2)) is Element of bool X
(X,(f * x1),x2) is Element of bool X

X is set
bool X is non empty set
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
f is set
x1 is set
y is Element of the carrier of ()
x2 is Element of bool X
(X,y,x2) is Element of bool X
f is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
x1 is Element of the carrier of ()
x2 is Element of bool X
f . (x1,x2) is Element of bool X
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
f . [x1,x2] is set
(X,x1,x2) is Element of bool X
y is Element of the carrier of ()
x is Element of bool X
(X,y,x) is Element of bool X
x1 is Element of the carrier of ()
x2 is Element of bool X
f . (x1,x2) is Element of bool X
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
f . [x1,x2] is set
(X,x1,x2) is Element of bool X
f is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
x1 is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
dom f is Relation-like the carrier of () -defined bool X -valued Element of bool [: the carrier of (),(bool X):]
bool [: the carrier of (),(bool X):] is non empty set
x2 is set
f . x2 is set
x1 . x2 is set
y is set
x is set
[y,x] is set
{y,x} is non empty finite set
{y} is non empty trivial finite 1 -element set
{{y,x},{y}} is non empty finite V34() set
l is Element of the carrier of ()
A is Element of bool X
f . (l,A) is Element of bool X
[l,A] is set
{l,A} is non empty finite set
{l} is non empty trivial finite 1 -element set
{{l,A},{l}} is non empty finite V34() set
f . [l,A] is set
(X,l,A) is Element of bool X
x1 . (l,A) is Element of bool X
x1 . [l,A] is set
dom x1 is Relation-like the carrier of () -defined bool X -valued Element of bool [: the carrier of (),(bool X):]
X is set
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of (X)
x1 is Element of the carrier of (X)
x2 is Element of the carrier of (X)
x1 + x2 is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
the addF of (X) . [x1,x2] is set
f + (x1 + x2) is Element of the carrier of (X)
the addF of (X) . (f,(x1 + x2)) is Element of the carrier of (X)
[f,(x1 + x2)] is set
{f,(x1 + x2)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(x1 + x2)},{f}} is non empty finite V34() set
the addF of (X) . [f,(x1 + x2)] is set
f + x1 is Element of the carrier of (X)
the addF of (X) . (f,x1) is Element of the carrier of (X)
[f,x1] is set
{f,x1} is non empty finite set
{{f,x1},{f}} is non empty finite V34() set
the addF of (X) . [f,x1] is set
(f + x1) + x2 is Element of the carrier of (X)
the addF of (X) . ((f + x1),x2) is Element of the carrier of (X)
[(f + x1),x2] is set
{(f + x1),x2} is non empty finite set
{(f + x1)} is non empty trivial finite 1 -element set
{{(f + x1),x2},{(f + x1)}} is non empty finite V34() set
the addF of (X) . [(f + x1),x2] is set
y is Element of bool X
x is Element of bool X
A is Element of bool X
x \+\ A is Element of bool X
x \ A is set
A \ x is set
(x \ A) \/ (A \ x) is set
y \+\ (x \+\ A) is Element of bool X
y \ (x \+\ A) is set
(x \+\ A) \ y is set
(y \ (x \+\ A)) \/ ((x \+\ A) \ y) is set
y \+\ x is Element of bool X
y \ x is set
x \ y is set
(y \ x) \/ (x \ y) is set
(y \+\ x) \+\ A is Element of bool X
(y \+\ x) \ A is set
A \ (y \+\ x) is set
((y \+\ x) \ A) \/ (A \ (y \+\ x)) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of ()
f + x1 is Element of the carrier of ()
the addF of () . (f,x1) is Element of the carrier of ()
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the addF of () . [f,x1] is set
f * x1 is Element of the carrier of ()
the multF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like V18([: the carrier of (), the carrier of ():], the carrier of ()) Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
the multF of () . (f,x1) is Element of the carrier of ()
the multF of () . [f,x1] is set
x2 is Element of the carrier of (X)
y is Element of the carrier of (X)
f * x2 is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
the lmult of (X) . (f,x2) is Element of the carrier of (X)
[f,x2] is set
{f,x2} is non empty finite set
{{f,x2},{f}} is non empty finite V34() set
the lmult of (X) . [f,x2] is set
x1 * y is Element of the carrier of (X)
the lmult of (X) . (x1,y) is Element of the carrier of (X)
[x1,y] is set
{x1,y} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,y},{x1}} is non empty finite V34() set
the lmult of (X) . [x1,y] is set
(f * x2) + (x1 * y) is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . ((f * x2),(x1 * y)) is Element of the carrier of (X)
[(f * x2),(x1 * y)] is set
{(f * x2),(x1 * y)} is non empty finite set
{(f * x2)} is non empty trivial finite 1 -element set
{{(f * x2),(x1 * y)},{(f * x2)}} is non empty finite V34() set
the addF of (X) . [(f * x2),(x1 * y)] is set
x2 + y is Element of the carrier of (X)
the addF of (X) . (x2,y) is Element of the carrier of (X)
[x2,y] is set
{x2,y} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,y},{x2}} is non empty finite V34() set
the addF of (X) . [x2,y] is set
f * (x2 + y) is Element of the carrier of (X)
the lmult of (X) . (f,(x2 + y)) is Element of the carrier of (X)
[f,(x2 + y)] is set
{f,(x2 + y)} is non empty finite set
{{f,(x2 + y)},{f}} is non empty finite V34() set
the lmult of (X) . [f,(x2 + y)] is set
(f + x1) * x2 is Element of the carrier of (X)
the lmult of (X) . ((f + x1),x2) is Element of the carrier of (X)
[(f + x1),x2] is set
{(f + x1),x2} is non empty finite set
{(f + x1)} is non empty trivial finite 1 -element set
{{(f + x1),x2},{(f + x1)}} is non empty finite V34() set
the lmult of (X) . [(f + x1),x2] is set
(f * x1) * x2 is Element of the carrier of (X)
the lmult of (X) . ((f * x1),x2) is Element of the carrier of (X)
[(f * x1),x2] is set
{(f * x1),x2} is non empty finite set
{(f * x1)} is non empty trivial finite 1 -element set
{{(f * x1),x2},{(f * x1)}} is non empty finite V34() set
the lmult of (X) . [(f * x1),x2] is set
x1 * x2 is Element of the carrier of (X)
the lmult of (X) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{{x1,x2},{x1}} is non empty finite V34() set
the lmult of (X) . [x1,x2] is set
f * (x1 * x2) is Element of the carrier of (X)
the lmult of (X) . (f,(x1 * x2)) is Element of the carrier of (X)
[f,(x1 * x2)] is set
{f,(x1 * x2)} is non empty finite set
{{f,(x1 * x2)},{f}} is non empty finite V34() set
the lmult of (X) . [f,(x1 * x2)] is set
x is Element of bool X
A is Element of bool X
(X,f,x) is Element of bool X
(X,x1,A) is Element of bool X
(X,f,x) \+\ (X,x1,A) is Element of bool X
(X,f,x) \ (X,x1,A) is set
(X,x1,A) \ (X,f,x) is set
((X,f,x) \ (X,x1,A)) \/ ((X,x1,A) \ (X,f,x)) is set
x \+\ A is Element of bool X
x \ A is set
A \ x is set
(x \ A) \/ (A \ x) is set
(X,f,(x \+\ A)) is Element of bool X
(X,(f + x1),x) is Element of bool X
(X,(f * x1),x) is Element of bool X
(X,x1,x) is Element of bool X
(X,f,(X,x1,x)) is Element of bool X
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of (X)
x1 is Element of the carrier of (X)
f + x1 is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (f,x1) is Element of the carrier of (X)
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the addF of (X) . [f,x1] is set
x1 + f is Element of the carrier of (X)
the addF of (X) . (x1,f) is Element of the carrier of (X)
[x1,f] is set
{x1,f} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,f},{x1}} is non empty finite V34() set
the addF of (X) . [x1,f] is set
y is Element of bool X
x2 is Element of bool X
y \+\ x2 is Element of bool X
y \ x2 is set
x2 \ y is set
(y \ x2) \/ (x2 \ y) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of (X)
x1 is Element of the carrier of (X)
f + x1 is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (f,x1) is Element of the carrier of (X)
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the addF of (X) . [f,x1] is set
x2 is Element of the carrier of (X)
(f + x1) + x2 is Element of the carrier of (X)
the addF of (X) . ((f + x1),x2) is Element of the carrier of (X)
[(f + x1),x2] is set
{(f + x1),x2} is non empty finite set
{(f + x1)} is non empty trivial finite 1 -element set
{{(f + x1),x2},{(f + x1)}} is non empty finite V34() set
the addF of (X) . [(f + x1),x2] is set
x1 + x2 is Element of the carrier of (X)
the addF of (X) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
the addF of (X) . [x1,x2] is set
f + (x1 + x2) is Element of the carrier of (X)
the addF of (X) . (f,(x1 + x2)) is Element of the carrier of (X)
[f,(x1 + x2)] is set
{f,(x1 + x2)} is non empty finite set
{{f,(x1 + x2)},{f}} is non empty finite V34() set
the addF of (X) . [f,(x1 + x2)] is set
y is Element of bool X
x is Element of bool X
A is Element of bool X
x \+\ A is Element of bool X
x \ A is set
A \ x is set
(x \ A) \/ (A \ x) is set
y \+\ (x \+\ A) is Element of bool X
y \ (x \+\ A) is set
(x \+\ A) \ y is set
(y \ (x \+\ A)) \/ ((x \+\ A) \ y) is set
y \+\ x is Element of bool X
y \ x is set
x \ y is set
(y \ x) \/ (x \ y) is set
(y \+\ x) \+\ A is Element of bool X
(y \+\ x) \ A is set
A \ (y \+\ x) is set
((y \+\ x) \ A) \/ (A \ (y \+\ x)) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of (X)
0. (X) is V50((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
f + (0. (X)) is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (f,(0. (X))) is Element of the carrier of (X)
[f,(0. (X))] is set
{f,(0. (X))} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(0. (X))},{f}} is non empty finite V34() set
the addF of (X) . [f,(0. (X))] is set
x1 is Element of bool X
x2 is Element of bool X
x1 \+\ x2 is Element of bool X
x1 \ x2 is set
x2 \ x1 is set
(x1 \ x2) \/ (x2 \ x1) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of (X)
f + f is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (f,f) is Element of the carrier of (X)
[f,f] is set
{f,f} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,f},{f}} is non empty finite V34() set
the addF of (X) . [f,f] is set
0. (X) is V50((X)) Element of the carrier of (X)
the ZeroF of (X) is Element of the carrier of (X)
x1 is Element of bool X
x1 \+\ x1 is Element of bool X
x1 \ x1 is set
(x1 \ x1) \/ (x1 \ x1) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of (X)
x2 is Element of the carrier of (X)
x1 + x2 is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
the addF of (X) . [x1,x2] is set
f * (x1 + x2) is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
the lmult of (X) . (f,(x1 + x2)) is Element of the carrier of (X)
[f,(x1 + x2)] is set
{f,(x1 + x2)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(x1 + x2)},{f}} is non empty finite V34() set
the lmult of (X) . [f,(x1 + x2)] is set
f * x1 is Element of the carrier of (X)
the lmult of (X) . (f,x1) is Element of the carrier of (X)
[f,x1] is set
{f,x1} is non empty finite set
{{f,x1},{f}} is non empty finite V34() set
the lmult of (X) . [f,x1] is set
f * x2 is Element of the carrier of (X)
the lmult of (X) . (f,x2) is Element of the carrier of (X)
[f,x2] is set
{f,x2} is non empty finite set
{{f,x2},{f}} is non empty finite V34() set
the lmult of (X) . [f,x2] is set
(f * x1) + (f * x2) is Element of the carrier of (X)
the addF of (X) . ((f * x1),(f * x2)) is Element of the carrier of (X)
[(f * x1),(f * x2)] is set
{(f * x1),(f * x2)} is non empty finite set
{(f * x1)} is non empty trivial finite 1 -element set
{{(f * x1),(f * x2)},{(f * x1)}} is non empty finite V34() set
the addF of (X) . [(f * x1),(f * x2)] is set
y is Element of bool X
x is Element of bool X
y \+\ x is Element of bool X
y \ x is set
x \ y is set
(y \ x) \/ (x \ y) is set
(X,f,(y \+\ x)) is Element of bool X
(X,f,y) is Element of bool X
(X,f,x) is Element of bool X
(X,f,y) \+\ (X,f,x) is Element of bool X
(X,f,y) \ (X,f,x) is set
(X,f,x) \ (X,f,y) is set
((X,f,y) \ (X,f,x)) \/ ((X,f,x) \ (X,f,y)) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of ()
f + x1 is Element of the carrier of ()
the addF of () . (f,x1) is Element of the carrier of ()
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the addF of () . [f,x1] is set
x2 is Element of the carrier of (X)
(f + x1) * x2 is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
the lmult of (X) . ((f + x1),x2) is Element of the carrier of (X)
[(f + x1),x2] is set
{(f + x1),x2} is non empty finite set
{(f + x1)} is non empty trivial finite 1 -element set
{{(f + x1),x2},{(f + x1)}} is non empty finite V34() set
the lmult of (X) . [(f + x1),x2] is set
f * x2 is Element of the carrier of (X)
the lmult of (X) . (f,x2) is Element of the carrier of (X)
[f,x2] is set
{f,x2} is non empty finite set
{{f,x2},{f}} is non empty finite V34() set
the lmult of (X) . [f,x2] is set
x1 * x2 is Element of the carrier of (X)
the lmult of (X) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
the lmult of (X) . [x1,x2] is set
(f * x2) + (x1 * x2) is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . ((f * x2),(x1 * x2)) is Element of the carrier of (X)
[(f * x2),(x1 * x2)] is set
{(f * x2),(x1 * x2)} is non empty finite set
{(f * x2)} is non empty trivial finite 1 -element set
{{(f * x2),(x1 * x2)},{(f * x2)}} is non empty finite V34() set
the addF of (X) . [(f * x2),(x1 * x2)] is set
y is Element of bool X
(X,(f + x1),y) is Element of bool X
(X,f,y) is Element of bool X
(X,x1,y) is Element of bool X
(X,f,y) \+\ (X,x1,y) is Element of bool X
(X,f,y) \ (X,x1,y) is set
(X,x1,y) \ (X,f,y) is set
((X,f,y) \ (X,x1,y)) \/ ((X,x1,y) \ (X,f,y)) is set
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of ()
f * x1 is Element of the carrier of ()
the multF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like V18([: the carrier of (), the carrier of ():], the carrier of ()) Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
the multF of () . (f,x1) is Element of the carrier of ()
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the multF of () . [f,x1] is set
x2 is Element of the carrier of (X)
(f * x1) * x2 is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
the lmult of (X) . ((f * x1),x2) is Element of the carrier of (X)
[(f * x1),x2] is set
{(f * x1),x2} is non empty finite set
{(f * x1)} is non empty trivial finite 1 -element set
{{(f * x1),x2},{(f * x1)}} is non empty finite V34() set
the lmult of (X) . [(f * x1),x2] is set
x1 * x2 is Element of the carrier of (X)
the lmult of (X) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
the lmult of (X) . [x1,x2] is set
f * (x1 * x2) is Element of the carrier of (X)
the lmult of (X) . (f,(x1 * x2)) is Element of the carrier of (X)
[f,(x1 * x2)] is set
{f,(x1 * x2)} is non empty finite set
{{f,(x1 * x2)},{f}} is non empty finite V34() set
the lmult of (X) . [f,(x1 * x2)] is set
y is Element of bool X
(X,(f * x1),y) is Element of bool X
(X,x1,y) is Element of bool X
(X,f,(X,x1,y)) is Element of bool X
1_ () is Element of the carrier of ()
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of (X)
(1_ ()) * f is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
the lmult of (X) . ((1_ ()),f) is Element of the carrier of (X)
[(1_ ()),f] is set
{(1_ ()),f} is non empty finite set
{(1_ ())} is non empty trivial finite 1 -element set
{{(1_ ()),f},{(1_ ())}} is non empty finite V34() set
the lmult of (X) . [(1_ ()),f] is set
x1 is Element of bool X
(X,(1_ ()),x1) is Element of bool X
X is set
(X) is non empty VectSpStr over ()
bool X is non empty set
(X) is Relation-like [:(bool X),(bool X):] -defined bool X -valued Function-like V18([:(bool X),(bool X):], bool X) Element of bool [:[:(bool X),(bool X):],(bool X):]
[:(bool X),(bool X):] is non empty set
[:[:(bool X),(bool X):],(bool X):] is non empty set
bool [:[:(bool X),(bool X):],(bool X):] is non empty set

(X) is Relation-like [: the carrier of (),(bool X):] -defined bool X -valued Function-like V18([: the carrier of (),(bool X):], bool X) Element of bool [:[: the carrier of (),(bool X):],(bool X):]
[: the carrier of (),(bool X):] is non empty set
[:[: the carrier of (),(bool X):],(bool X):] is non empty set
bool [:[: the carrier of (),(bool X):],(bool X):] is non empty set
VectSpStr(# (bool X),(X),({} X),(X) #) is non empty strict VectSpStr over ()
the carrier of (X) is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of (X)
x2 is Element of the carrier of (X)
x1 + x2 is Element of the carrier of (X)
the addF of (X) is Relation-like [: the carrier of (X), the carrier of (X):] -defined the carrier of (X) -valued 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) . (x1,x2) is Element of the carrier of (X)
[x1,x2] is set
{x1,x2} is non empty finite set
{x1} is non empty trivial finite 1 -element set
{{x1,x2},{x1}} is non empty finite V34() set
the addF of (X) . [x1,x2] is set
f * (x1 + x2) is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):] is non empty set
the lmult of (X) . (f,(x1 + x2)) is Element of the carrier of (X)
[f,(x1 + x2)] is set
{f,(x1 + x2)} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(x1 + x2)},{f}} is non empty finite V34() set
the lmult of (X) . [f,(x1 + x2)] is set
f * x1 is Element of the carrier of (X)
the lmult of (X) . (f,x1) is Element of the carrier of (X)
[f,x1] is set
{f,x1} is non empty finite set
{{f,x1},{f}} is non empty finite V34() set
the lmult of (X) . [f,x1] is set
f * x2 is Element of the carrier of (X)
the lmult of (X) . (f,x2) is Element of the carrier of (X)
[f,x2] is set
{f,x2} is non empty finite set
{{f,x2},{f}} is non empty finite V34() set
the lmult of (X) . [f,x2] is set
(f * x1) + (f * x2) is Element of the carrier of (X)
the addF of (X) . ((f * x1),(f * x2)) is Element of the carrier of (X)
[(f * x1),(f * x2)] is set
{(f * x1),(f * x2)} is non empty finite set
{(f * x1)} is non empty trivial finite 1 -element set
{{(f * x1),(f * x2)},{(f * x1)}} is non empty finite V34() set
the addF of (X) . [(f * x1),(f * x2)] is set
the carrier of (X) is non empty set
f is Element of the carrier of ()
x1 is Element of the carrier of ()
f + x1 is Element of the carrier of ()
the addF of () . (f,x1) is Element of the carrier of ()
[f,x1] is set
{f,x1} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,x1},{f}} is non empty finite V34() set
the addF of () . [f,x1] is set
x2 is Element of the carrier of (X)
(f + x1) * x2 is Element of the carrier of (X)
the lmult of (X) is Relation-like [: the carrier of (), the carrier of (X):] -defined the carrier of (X) -valued Function-like V18([: the carrier of (), the carrier of (X):], the carrier of (X)) Element of bool [:[: the carrier of (), the carrier of (X):], the carrier of (X):]
[: the carrier of (), the carrier of (X):] is non empty set
[:[: the carrier of (), the